Is this sentence correct? How about 我和同学一起常学习。?
Neither is perfect. The orders we often choose are >> 我和同学常常一起学习 or 我常常和同学一起学习 or 我和同学常一起学习 or 我常和同学一起学习。(No big difference between 常 and 常常. )
Are these sentences correct?
Yeah both correct, 周末 actually. It's like in English >> At weekend what do you do & What do you do at weekend.
In this sentence, 上班的时候 means when you go to work? or while you go to work?
I didn't get what this sentence meant but yeah, it's when you go to work, actually I don't think we say 'while you go to work' often in English.
Is it okay to use 有点儿 instead of 一点儿?
No it's exceedingly not OK, but in some cases eg both 我有点累 and 我有一点累 are OK.
Your original sentence is kinda unnatural btw,
>> 上午我只吃一点面包，喝一杯咖啡。So better be without the 和 in the middle, but the original is OK too, this means it's your habbit, you do this every day, it's regular.
>> 上午我只吃了一点面包，喝了一杯咖啡。This means what happened this morning, only this morning, the past tense.