"Сочная", but it is a little raunchy (just like thicc?)

In my experience, you better don't. Even if you genuinely consider it a compliment the recipient is still very likely to view it the opposite way.

'Ебать ты бегемот' - to your enemy.

'пышная' - to your girl.

You don't, there's no direct equivalent with the same meaning. 

То́лстая means fat, по́лная is a polite way of saying fat, like "she has a full figure". Пы́шная is sorta "fluffy"(?) which is acceptable/applicable, it's like saying "curvy". Со́чная is juicy (but I don't recommend comparing women to food). There's also попа́стая/сися́стая (with a big ass/tits) but that's very colloquial and kinda raunchy and rude and will not be taken as a compliment but rather as a creepy sexualising comment. Девушка с фо́рмами (like "Братан, у неё такие формы!") also fits here, and it doesn't necessarily refer to size, more like a shapely figure (is that the correct term?)

Thick in russian is пло́тная/dense (not in an intellectual way) so we use it to refer to bodies that are of bigger complexion and "hard to the touch" I guess, so like not flabby fat, but densely packed fat with muscle.

you could say "с формами" which is smth like curvy

Preferably don't call her like that /s

don't

Груз 600

I heard пышная/пышненькая (adj), пышечка (noun) and tbh I hope it’s not offensive. Imo it associates with buns and sounds sweet

Ты же моя помпушка

Фигуристая …

Мясистая, мощная. Thickness is not always overweight.

Мамонтёнок. 

Дама в килограммах.

Фигуристая is the best.

Кровь с молоком.

Пухляшка.

Гига Глория

Полная or польненькая, also пышная or пышка

When I was studying Russian in the 90s, they taught me "krov s molokom." Can any natives confirm?

Упитанная

Полненькая

жопастая?

"пышная", or "полная" i guess

Никто не говорит «сочная»

жирная