Yes. If you've accepted a job it would look bad to inquire about another opportunity at any point inside the first year, much less before you even start. Honor what you've accepted, kick *** at that job, then inquire about other opportunities. IF you kick *** at your job they will want to keep you happy and will listen if you want to try something else.

Don't do it before you even start, no. A lateral move can be asked about 6 months into your working there.

Yes

Yes it would look bad. It would look like you don't WANT the job you got - and people who don't want the job don't make very good employees.

Do the job for awhile and then after you've established yourself as a good worker and have scoped out the company culture, THEN you can apply for a move within the company once it's safe.

get your foot in the door first and then you can start looking