Freed

Normals
5A - Fast and very slight advantage. Will wiff crouching shorties, so can be used for fake-hit throw setups.
5B - Forces standing on hit. Useful for a number of combos. Can chain to c.C if close enough.

c.C - Really, really fast. Can be canceled late, useful for combos.
f.C - Strong but will wiff on crouching shorties. Can be useful for anti-jump.
2C - Great long range poke. Can't really hit confirm reliably with it, but very strong damage by itself anyway.

5D - Good Anti-Air kick. Nothing remarkable about it otherwise though.
2D - Big sweep. Really unsafe though, so not really that useful.

j.B - Small crossup. Useful, but hard to use correctly.
j.C - Extremely small crossup, not worth the effort of trying to use as one.
Chains
5A 2D
5A 2A ...
2A 2A ...
2A 5A ...
5B c.C
Specials
[4]6 A/C - Magnum Jetter
Dashing punch attack. Strong and can be hard (or impossible) to punish if spaced right. Wiffs on crouching shorties which is very unfortunate, see this chart for details.
C version is slower, stronger, covers more distance, and knocks down (but is techable).
[4]6 B/D - Phantom Dive
Dashing overhead. Is reversal invincible to Projectiles, until the swing begins. Safe on block. Launches on Counter Hit for easy followups. Somewhat slow, so you will have to be very tricky to hit with it.
D version is slower, travels farther, and is stronger. Could be useful to bait Gatchis?
[4]6 Hold B/D - Phantom Glide
Hold the attack button to instead do a dashing low attack. Very slow, knocks down. Also reversal invincible to Projectiles until swing begins.
D version is slower, travels farther, and is stronger.
[2]8 A/C - Welcome Tempest
Uppercut style attack, launches when hits and can possibly be followed up on. Very unsafe on block.
A version is very fast but has no special properties otherwise. Use as AA when possible.
C version is a two-uppercut style attack. Has reversal invincibility above the foot through the first hit. Can go under every projectile in the game, and will cleanly beat everything but some low normals.

Supers

236236P - Magnum Jet Landing
Super version of the Magnum Jetter. Good for ending some combos, but much weaker in combos than Heat My Justice is. Unlike the regular Magnum Jetter, this will hit crouching shorties.
236236K - Heat My Justice
Fast Vertical strike, finishes with a very powerful beam attack on hit. Somewhat slow startup and very short horizontal range, but the damage is great. Not a reversal, and can be parried (or thrown) on reaction.
Heat Up
While in Heat Up, Freed's special moves will have a shadow double mimic what you do. The primary use of this is very strong pressure and mixups.
Note that even with the Phantom Dive or Glide specials, the shadows will never hit high or low, they can be blocked either way.

Enhanced Specials

[4]6 A/C - Magnum Jetter
Shadows hit much lower than the physical hit, so they will connect with crouching shorties.
A version is very good for combos and can be linked off of.
C version no longer knocks down, shadow is very delayed and can be used for very strong Oki.
[4]6 B/D - Phantom Dive
Does not knock down anymore. Both version can be comboed off of.
[4]6 Hold B/D - Phantom Glide
D version can be comboed off of on Counter Hit. But otherwise, pretty much useless.
[2]8 A/C - Welcome Tempest
C version is faster, can combo off of 2C easily. Very useful for combos.

Mixups and Setups

Freed makes good use of Instant Heat Up for setups and mixups. Some examples are:
[4]6 B+A+C ...
(Overhead)
[4]6 C+B+D (wiff) ...
(Setup for Low, Throw, or Jump In)
[4]6 D+A+C (wiff) ...
(Similar but much slower setup)

As an important note, due to how the buffering in this game works, you must time your instant heat up carefully (especially of a throw) to avoid getting the wrong move to come out. You may get [4]6D by accident instead of [4]6C if you input the motion too early after a throw, for example.

Aside from the basic mixups into combos, it's important to understand how to react if they block your mixups. Continuing your rushdown even when something doesn't work the first time is essential for using Freed. Some examples are:
Blocked [4]6B -> [4]6B
Blocked [4]6B or [4]6A -> 66 Throw
Blocked [4]6B or [4]6A -> 66 5B c.C, [4]6A/B ...
Blocked [4]6B or [4]6A -> 2B [4]6A ...
Blocked [4]6D or [4]6C -> 66 Jump ...

(??) Reset Ground Chains? For examples of combos, see the Heat Up Combos section.
Combos

Basics

2A 2A 2A [4]6A
Doesn't work on crouching shorties, but effective and easy to hit confirm against tall characters.
2A 5A 2D
If done close, can hit some additional characters who are crouching. Never works on Marco, Ashley, Coyori, or Cedric.
2C 236236P
Good for long range punish, will hit anyone.
(mid)
2B [2]8A
(corner)
2B [2]8A, c.C Reset
Can't really hit confirm and unsafe on block. More plausible after a jump-in attack but that's about it.
5B c.C [4]6C (236236P/K)
Works on anyone. Strong combo. Heat My Justice does more damage but generally only combos in the corner.
66[4] 5B c.C
(pause)
[4]6C (236236P/K)
Tricky combo. To get the Magnum to come out properly, you must delay canceling the c.C. Very useful to learn as it gives you the ability to do stronger punishes after a dash.
AA [2]8A, [4]6C

CH [4]6B/D, [4]6C
CH [4]6B/D, [2]8C
CH [4]6B/D, 236236P
CH [4]6B/D, 66 236236K
Last combo here has somewhat tight timing, and as such may not be practical to do on reaction unless in the corner where you can omit the dash.

Gatchi Counter

(1 close)
c.C 236236K
[1554]
(1 far)
2C 236236P
[1115]

High Gatchi Drive

(0 any)
j.D |> 6, c.C, [4]6C
[867]
(0 mid)
6, c.C, Jump, (late) j.D, [2]8C
[933]

(1 any)
j.D |> (66) c.C 236236K
[1333]
(1 mid)
6, c.C, [4]6C 236236K
[1464]

Low Gatchi Drive

(0+ corner)
66, 5B c.C f.C 2C [4]6C (236236K)
[?/?]
(0+ mid)
66 Jump, j.C j.D |> (5B) c.C f.C 2C [4]6C (236236P/K)
[1297/1909/2055]

Heat Up

Generic Combos:
(Mid)
[4]6B, 2C [2]8C, [4]6C
(Near Corner)
[4]6B, 2C [2]8C, [4]6A (wiff), c.C Reset ...
Physical hit of [4]6A must wiff, but the Shadow hit will connect.
(Mid)
2B [4]6A, [4]6A, 5B [4]6A, [4]6A, 2C [4]6C
(Mid)
2B [4]6A, [4]6A, 5B [4]6A, [4]6A, 2C 236236P, c.C Reset ...

From Neutral:
[4]6 B+A+C, 2C [2]8C, [4]6C or c.C Reset ...
(Overhead)

From c.C Reset:
... c.C [4]6C (wiff), 4, 2B [4]6A [4]6A
(Low)
... c.C [4]6C (wiff), 2B [2]8A, [2]8C or c.C or 236236K
(Low, More Risky)
... c.C [4]6C (wiff), [4]6B, 2C [2]8C, [2]8C or c.C Reset ...
(Overhead)
... c.C [4]6C (wiff), 4, 66 Throw
(Throw)
... c.C [4]6C (wiff), 5A (wiff) Throw
(Fake Hit Throw)
If you get to a reset without Heat Up, you can instant activate it instead by doing c.C, [4]6C+B+D as a link.
If you get to a reset and your Heat Up ends at the [4]6C, you can reactivate it and keep going as usual.

Off a Throw or Knockdown:
[4]6 C+B+D, 4, 2B [4]6A, [4]6A, 5B [4]6A, [4]6A, 2C [4]6C
(Low)
[4]6 C+B+D, 4, 66 Throw, Repeat ...
(Throw)
[4]6 C+B+D, Neutral Jump, Late j.D |> 5B [4]6A, 5B [4]6A [4]6A ...
(Jump In)
[4]6 C+B+D, Neutral Jump, |> 2B [4]6A, [4]6A, 5B [4]6A, [4]6A ...
(Fake Jump In)
[4]6 C+B+D, Late Jump, Crossup j.B |> 5B [4]6A, [4]6A, 5B [4]6A, [4]6A ...
(Fake Crossup)
[4]6 C+B+D, Early Jump, j.B |> 5B [4]6A, [4]6A ...
(Real Crossup)

[4]6 D+A+C, Throw
(Throw, Risky)
[4]6 D+A+C, 5B c.C [4]6A, [4]6A, 5B [4]6A, [4]6A ...
(Hit)