Supposed to is part of a modal verb phrase meaning expected to or required to. Suppose (without the d) should only be used as the present tense of the verb meaning to assume (something to be true).

“Used to” is used for positive statements or negative statements with “never”: “I used to work for Company X, but I left in 2015” “I never used to go jogging, but now I go twice a week” “Use to” is used for questions and negative statements with “didn’t”: “Where did you use to go on vacation when you were a kid?” “I didn’t use to follow politics, but now I try to keep up” I would say that the majority of native speakers don’t know this, however, for two reasons: the forms with “used to” are more common, but more importantly, the pronunciation of both is exactly the same! It’s possible that “supposed to” and “suppose to” follow the same form, but I’d have to do some research to be sure.

"What am I suppose" as in 'what am I suppose to do?' is incorrect. The correct form is "What am I supposed (to do)?" However, you will often see the incorrect form written down. The two forms have identical pronunciations so many people who have only heard it write it incorrectly. This is also why some people incorrectly write "I use to ..."

We use used to when we refer to things in the past which are no longer true. Use to typically occurs with did; "did you use to work there?

"What am I supposed" + verb in infinitive means "What should I..../ What I am required to do?" I've never heard "What am I suppose." Are you sure you saw / heard this from a native English speaker? "Do you suppose...." exists. to be used to - to be accustomed to (I am used to my wife asking me where her keys are) to get used to - to become accustomed to (I took me a long time to get used to Spanish traditions) used to - past tense (I used to live in the U.S.) to use to / for = to utilize something (I use a can opener to open cans)