A short answer to the title of your question would be that you do not lose the right to appeal against any of the arbiter's decisions by signing the scoresheet.
But also notice that you did not use your right to appeal anyway, therefore, you have, most likely, already lost it. Every tournament has an appeal committee and players wishing to appeal must do so usually within an hour of the end of the game or maybe within an hour of the end of the round or something like that, you can check with the arbiter. FIDE is not the appeal authority thus sending a letter to them did not serve any other purpose than to merely complain about the arbiter without having actually used all the means that were available to you.
What to do next time. If you suspect that your opponent is cheating - a very strong accusation that you should not make lightly, you could actually be penalized by FIDE for a false accusation - then talk to the arbiter as soon as possible and several times if necessary. However, notice that if you insist that your opponent is cheating then you will be required to make this claim in writing. There is a form that you need to fill in, sign it, and it will be sent to FIDE.
When you complain to the arbiter, there is only so much they can do, however. While they will take your complaint seriously, they will not accuse your opponent of cheating without having a good reason, i.e. they will need to see some evidence of highly suspicious behaviour themselves. In practice this means that the arbiter will attempt to observe the player for the rest of the game (and possibly even in the next rounds) but you cannot expect the arbiter to forfeit the player on your request. In my view, based on your description of the situation, the arbiter did the right thing - they inspected the situation and they warned the player.
Your opponent talking to other people. This is somewhat tricky, although it is forbidden to take advice from anyone during the game players always talk to other people in the playing hall. This is very common and you do not want to forfeit everyone who you observe talking to someone. Being strict makes sense in some important tournaments and less sense in leisure tournaments. I am not saying that the arbiter should not act, they should. But most of the time it is difficult for them to establish how innocent the conversation was and what (if any) damage was done. Thus the appropriate course of action is to warn the players and perhaps keep an eye on them.
What you did not mention is that your opponent was a ten-year-old child and I guess the other three or four guys you mention were similarly aged children. In theory this does not matter, in practice, however, it is unrealistic to expect children to stay focused for a number of hours and not to talk to anyone. And you certainly do not want to forfeit the child for mere talking to someone (or even worse for others talking to him), no children would play chess then. With children, most of the time it is enough to warn them. And if you do not like them gathering at your board and talking to your opponent then tell them. Most children have respect from adults.
A personal story. Once I played a league and my opponent was not happy about losing his advantage in the game or something like that. He made a move, left the room and then I heard him complaining about the game to other people outside. Not a big deal but it was disturbing me. Thus I went out and told them to go to talk about it somewhere else where I couldn't hear them. They were very embarassed, problem solved.