Does an acceptance of an abstract mean that I will definitely be presenting at the conference?
The practices vary significantly by field, but unless it is a very unusual case, having your abstract accepted means that you will be presented in some form or another.  It is not certain, however, whether you will be making an oral presentation.

In some meetings, having your abstract accepted means that you are definitely going to be getting up on stage and presenting.  In others, it means that you will definitely not be presenting, but will be given a chance to stand next to a poster in a distant corner of a giant room where nobody will realize that you are even there.  Most are somewhere in the middle, and you cannot know where it will fall on that spectrum without asking the organizers or looking at information from past conferences.

In all cases, however, it is reasonable to approach your advisor / department to ask about travel support.  Whether you can get full support depends on their policies and finances.  If you cannot, many conferences also have student travel grants or opportunities to work as a conference volunteer in return for having some of your costs compensated.