In commercial business "adet" is used. Forexample, you note down your stock, you say "10 adet televizyon, 20 adet bulaşık makinesi, 5 adet buzdolabı ...). It sounds more professionnal.

bitmek is an intransitive (requires no object) verb and bitirmek is transitive one ( requires an object)

bitmek= come to an end, to be over, to use up something

film bitti = movie has ended

ekmek bitti = no bread is left

iş bitti = work is over

program bitti = program has ended

okul bitti = the school is over (it is closed)

bitirmek = finish, make it come to an end

işi bitirdi = he has completed the job

ekmeği bitirdi = he has used all the breads

filmi bitirdi = he has finished the movie

programı bitirdi = he has finished the program

okulu bitirdi = he has finished the school (graduated from the school)

also

sona ermek = to end

program sona erdi = program has ended

ılık olanını beğenir misiniz?

would you like the warm one (not cold not hot)?

ılık olanını ister misiniz? would be better in Turkish.

 When a movie is finished, we say film bitti.  When we say did you finish your food? then it means yemeğini bitirdin mi?  I think if finishing actions happen by themselves, we use bitmek.. but when we do the action we use bitirmek.

Bitmek has also some other meanings, you can check the dictionary for them.

regarding -ılık olanını beğenir misin? can you be more specific about it... what is the first word?   If you can not, then it approximately means something like "would you like the one which is......?"