Your sentences are generally okay but some needs refinement.
1. 나는 시험에 무슨 문제가 나올지 예상(이) 안 돼 [= 예상이 안 돼]. (no English expression with the same structure)
예상되다 or 예상이 되다 is in passive form, as in something is expected. In this case, 예상이 되다 is better.
- 나는 시험에 무슨 문제가 나올지 예상 못해 (를 -> 가. 나오다 is intransitive) = I can't predict/guess what questions will be in the exam.
This kind of "I try but can't quite ..." or "can't seem to ..." is better said with the -겠어 form (못해 is used for clear-cut impossibility of lacking the ability or circumstances preventing you). So 예상(을) 못하겠어 would be better here.
2. 나는 네가 몇점이 받을지 예상돼. (이 -> 을. 받다 is transitive requiring an object).
나는 네가 몇점을 받을지 예상할 수 있어. GOOD
예상되다 and 예상이 (안) 되다 may be a little difficult to use perfecttly. There are two common uses.
1. something is generally/officially expected (used a lot in news reports). This is usually expressed as 예상되다 (single word). "내일은 아침부터 비가 많이 올 것으로 예상됩니다". Passive voice works well because the entity doing the prediction is often not clear, it's often some long name institution.
2. you have a/no personal hunch about some outcome. This is typically said as 예상이 (안) 되다 form. 이번 결승전은 어떻게 될 지 예상이 안 돼 (leaving 이 in adds emphasis). This case is probably more often said in the active voice too, as in 예상[or 짐작, 상상]을 못하겠어 or 예상/짐작/상상을 할 수가 없어.