Does what I did, hugging a boy from behind with masturbation, constitute sodomy (liwat) that necessitates the legal punishment (hadd), and will my repentance be accepted given the overwhelming lust and my commission of other sins, and how can I repent?

Legally (in Islamic law), sodomy (liwat) is defined as the insertion of the glans into the anus of a male. What was done is not sodomy according to Islamic law, but it is forbidden and falls under the purview of His (Allah's) saying, "And whoever seeks beyond that – then those are the transgressors" (Quran 23:7). It is also a prelude to sodomy, which is considered one of the gravest major sins, forbidden, and contrary to human nature (fitra). The door to repentance remains open as long as a servant has not gargled (i.e., is not on his deathbed) or the sun has not risen from its west. Sincere repentance (tawbah nasuh) includes regret, abandonment of the sin, and a firm resolve not to return to it. Allah accepts the repentance of the wrongdoer and transforms evil deeds into good deeds for the repenting believer.