Is it permissible to give charity on behalf of a deceased mother and other deceased individuals, and what is the virtue of that for the one giving the charity, knowing that the one giving the charity feels that giving charity on their own behalf might increase their sins?

Giving charity on behalf of one's parents is an act of piety and benevolence. The reward for charity reaches the deceased without diminishing the reward of the one who gives it. What the questioner feels about an increase in sins is merely a baseless whisper (waswas), and he should continue to show filial piety to his mother through supplication and by giving charity on her behalf and on behalf of all deceased Muslims.