What should I do about my feeling that people are ridiculing me when I do good deeds or wear the abaya, and are my actions considered mockery of God that takes me out of the fold of Islam?

There is no mockery in what was mentioned, and the warning is against thegivings that lead to great evil. Fears of people's mockery are delusions from Satan, and it is advised to ignore them and act naturally. If the action is an approach to Allah, then the ridicule of others does not harm, and its woe is upon them, and a Muslim does not care for people's رضا or their displeasure if his intention is to please Allah.