Are there other explanations of ”right hand” than masturbation (Matthew 5:30)? The context in Matthew 5:30 strongly suggests that Jesus is talking about adultery. Verse 21 starts with "You have heard", starting a section about respecting your neighbor. Again, Verse 27 starts with "You have heard" and starts a section about adultery. The next section after that starts at verse 33 with similar words "Again, you have heard". All these sections concentrate on one issue. Also, the word "again" in verse 33 emphasizes the fact that these are separate sections.

Therefore it's quite clear that verses 27-30 are related to adultery, and 31-32 are a continuation of that theme. Also, verse 28 makes it clear that verse 29 is about lusting with the eye. Then verse 30 is very similar to verse 29, only different body part.

Given these observations above, it's clear for me that Jesus is banning masturbation. My question is that could "right hand" mean something else, also? 

Remember that Jesus is talking about adultery, or to put in another way, not meeting the sexual needs of your spouse. The spouse is neglected against in both masturbation and adultery with another person (masturbation is kind of adultery, too).

So, is there any other possible meaning for the ”right hand” in verse 30, considering the context?

I’m a fundamentalist protestant, having not found a denomination with perfect theology yet. I just want to know if any Bible-believing Christian has found another explanation (based on Bible and this context) for the right hand, other than masturbation.

Matthew 5:27-30: 27. “You have heard that it was said, ‘YOU SHALL NOT COMMIT ADULTERY’; 28.but I say to you that everyone who looks at a woman with lust for her has already committed adultery with her in his heart. 29.“If your right eye makes you stumble, tear it out and throw it from you; for it is better for you to lose one of the parts of your body, than for your whole body to be thrown into hell. 30.“If your right hand makes you stumble, cut it off and throw it from you; for it is better for you to lose one of the parts of your body, than for your whole body to go into hell.
Let's look at the narrow context:


  Adultery
  
  27 “You have heard that it was said, ‘You shall not commit
  adultery.’ 28 But I tell you that anyone who looks at a woman
  lustfully has already committed adultery with her in his heart. 29 If
  your right eye causes you to stumble, gouge it out and throw it away.
  It is better for you to lose one part of your body than for your whole
  body to be thrown into hell. 30 And if your right hand causes you to
  stumble, cut it off and throw it away. It is better for you to lose
  one part of your body than for your whole body to go into hell.


Matthew 5:28 obviously states that an adulterous thought or look is a sin in itself. 

Now, an act is of greater significance than thought. Masturbation is an act in line with adulterous thought, furthermore, it implies it most of the time.

I don't know if 'the right hand' had an implication in Hebrew as it does in Croatian (I don't even know if it has a sexual implication in English), so I won't take that as an implication forbidding masturbation.

The whole passage is also a very cautious one. It encourages you to take measures to prevent yourself from sinning. In light of that, we can also conclude you shouldn't masturbate, at least as a precaution since you are having doubts if it is sinful.

If you aren't just interested in Matthew 5, Genesis 38:8-10 clearly implies sexual acts against nature (not leading to procreation), such as masturbation and contraception are sinful.

However, that is just my opinion, so I'll leave you with something of actual worth.
The Catholic Church's binding teaching (not defined here, but condensed in the CCC):


  CCC 2352 By masturbation is to be understood the deliberate
  stimulation of the genital organs in order to derive sexual pleasure.
  "Both the Magisterium of the Church, in the course of a constant
  tradition, and the moral sense of the faithful have been in no doubt
  and have firmly maintained that masturbation is an intrinsically and
  gravely disordered action." "The deliberate use of the sexual faculty,
  for whatever reason, outside of marriage is essentially contrary to
  its purpose." For here sexual pleasure is sought outside of "the
  sexual relationship which is demanded by the moral order and in which
  the total meaning of mutual self-giving and human procreation in the
  context of true love is achieved."


Here is also the passage on contraception:


  2370 Periodic continence, that is, the methods of birth regulation
  based on self-observation and the use of infertile periods, is in
  conformity with the objective criteria of morality.158 These methods
  respect the bodies of the spouses, encourage tenderness between them,
  and favor the education of an authentic freedom. In contrast, "every
  action which, whether in anticipation of the conjugal act, or in its
  accomplishment, or in the development of its natural consequences,
  proposes, whether as an end or as a means, to render procreation
  impossible" is intrinsically evil:
  
  > Thus the innate language that expresses the total reciprocal self-giving of husband and wife is overlaid, through contraception, by
  an objectively contradictory language, namely, that of not giving
  oneself totally to the other. This leads not only to a positive
  refusal to be open to life but also to a falsification of the inner
  truth of conjugal love, which is called upon to give itself in
  personal totality. . . . The difference, both anthropological and
  moral, between contraception and recourse to the rhythm of the cycle .
  . . involves in the final analysis two irreconcilable concepts of the
  human person and of human sexuality.


I encourage you to read the context in the Catechism.