Can a Doppelganger buy Changeling racial feats

The formula is that you have to pay for an ability score the new modifier. So going from 7 to 6 gives you a price of -2, 6 to 5 and 5 to 4 each give you -3, and so on. Dropping an ability score to 3 would give you 16 points.

Score | Mod | Cost  
   10 |   0 |    0
    9 |  -1 |    1
    8 |  -1 |    2
    7 |  -2 |    4
    6 |  -2 |    6
    5 |  -3 |    9
    4 |  -3 |   12
    3 |  -4 |   16

It's uncertain whether those values would be balanced ; while they follow the pattern of ability score costs, nothing says that this pattern won't fall apart outside of the 7-18 range. Furthermore, in any case, this should never be an option available to players as discussed in the answer to this question.

You also don't need to sleep, and don't suffer exhaustion from lack of rest.

I believe this could be abused.

Suppose a Slimefolk Sorcerer/Warlock uses Flexible Casting to convert Warlock Spell Slots to Sorcerer Points then to Spell Slots. The Slimefolk can then short rest to gain more Warlock Spell Slots via Pact Magic, repeating this cycle.

Normally this can be contained because eventually a player either becomes exhausted or is forced to take a long rest. All other races sleep once a day to avoid exhaustion, except Elves who mediate for 4 hours and gain the effects of 8 hours of sleep.

A Slimefolk could stay up for days, weeks, months, years, accumulating god knows how many Spell Slots.

This may not seem like a big deal because you won't let your Slimefolk do this, but what are you going to do when the party wants to take a long rest? The Slimefolk will inevitably opt to take 8x short rests. Once the rest of the party has finished their long rest the a Slimefolk with Sorcerer 2/Warlock 1 would have 11 level 1 Spell Slots.

I suggest the Slimefolk needs an equivalent mechanic to the Elf's Trance, forcing them to take a Long Rest once per day. Here is my suggestion:

Ooze Nature

Your creature type is both humanoid and ooze.

You also don't need to sleep, and don't suffer exhaustion from lack of rest. However maintaining a form for a long period can cause exhaustion, so for 4 hours per day you must return to being an immobile puddle of goo. After, you gain the same benefit as a human does from 8 hours of sleep and when you finish resting you can choose a permanent form as if you were the target of the Alter Self spell.

The wording could use some work, but I'm sure you see the intent.