Must repentance be accepted by Gd? Is sincere repentance always accepted? Is repentance a form of prayer? (Not all prayer is accepted.)
Tosafos in Bava Metzia 58b (ד"ה חוץ) says that Teshuva/repentance works for everything (תשובה מועלת לכל דבר). However, it is important to note that teshuva will not save somebody from any punishment in beis din/court. It is also important to note that the Zohar says that teshuva does not work for the sin of spilling one's seed/הוצאת זרע לבטלה, but see the Bnei Yisaschar's piece on Shovavim where he discusses this concept at length that one can repent for that sin, but teshuva does not do a full rectification of what damage was done in the Heavens for such an act.
Also, the Sages tell us that one cannot sin and bank on the fact that they will repent later, so for such a sin teshuva will not help. The Avnei Nezer says this is one reason that some people (typically people who daven Ashkenaz) do not say Vidui every day before Tachanun.
another source from the shaar teshuva in the chovos halevavos:
Repentance is not withheld from a sinner, rather the obstruction comes from his own wickedness and deceitful heart. But if he sincerely wants to draw near to G-d, the gate of repentance will not be closed before him, and no obstacle will prevent him from reaching it. Rather, G-d will open for him the gate of the just, and teach him the good path in His mercy and in His goodness, as written "Good and upright is the L-ord: therefore will he teach sinners in the way" (Tehilim 25:8), and "from there you will seek the L-ord your G-d, and you will find Him, if you seek Him with all your heart and with all your soul" (Devarim 4:29), and "Rather,[this] thing (repentance) is very close to you; it is in your mouth and in your heart, so that you can fulfill it" (Devarim 30:14), and "The L-ord is near to all who call upon Him, To all who call upon Him in truth" (Tehilim 145:18).
there he goes into even the difficult cases such as murder, or fathering a mamzer and explains that even so his teshuva will not be rejected.