Omega Geneve Dynamic Lady HELP

Good morning everybody,
I recently purchased this watch for my gf on an auction site (Catawiki). The seller said the movement had a 1 year warranty provided by a private but i received no confirmation about that whatsoever. The watch seems in good shape, my concern about the movement is that the crown only seems to have one position, and it directly changes the hour, not the date. I haven't tried to apply much force on it in order to preserve the watch, also the crown seems a bit loose when put in said position. I also have concerns regarding the bracelet, since it has no spare links and i fear it may be too tight. My questions are: where should i bring this watch to be serviced? I fear Omega might ask too much money, also do you hink i could find a spare bracelet? I don't care if that's original or not, i just want it to fit. I'm new to watch collecting so please be patient with me.
I than everybody who will answer me!

It's no need at all to go to an Omega service.. I am sure that you have near your location several independent watchmakers who can do the job.
Regarding the bracelet will be difficult to spot the original bracelet but you can try on ebay after the searching of reference number. If the bracelet is authentic inside the clasp you will see some numbers which represent the reference number of the bracelet. Welcome to the forum!

Dear Lucian23, coming back to you after several months, sorry for the late reply. I still haven't serviced the watch in the end, it looks like it's running a little bit fast, i'll have it checked out by an independent watchmaker as you suggested. The bracelet fit nicely to my girlfriend's wrist, and it shows the omega logo anche a serial number so i'm inclined to considering it authentic. Thanks alot for welcoming me, i'm so sorry for the late answer!!

Normal for that movement (probably a 681 or 684) to only have one position. You "quick set" the date by flipping the time between 8pm and 1am. I have 2.