Ninajaribu kujisomfunza Kiswahili.

I'll focus on your use 'kujisoma' here. 'Ku' makes it a infinite verb while ~ji~ indicates the target of the action (in this case oneself). So Kujisoma would translate to 'to read oneself' which doesn't really work in this context. Dropping the ~ji~ prefix would probably make it sound more natural but still miss the meaning of 'teaching oneself Kiswahili'. So, the verb to use here is ~funza or rather ~jifunza

Ninapenda langu ya Kiswahili.

Nimefurahi kukutane nawe!

Nimefurahi kukutana nawe is fine. You could also say 'Ni furaha kukutana nawe'