[not a teacher]
1) The answer to “Tries or is trying” depends on what you are trying to say. Here are some variations.
a) three items:
“We are not afraid to speak, we make many efforts, and we try to build well-balanced sentences."
b) two phrases, second has two items (notice the switch to the semicolon):
“We are not afraid to speak; we make many efforts and try to build well-balanced sentences."
c) two phrases, second has one item:
c.1) “We are not afraid to speak; we make many efforts to try to build well-balanced sentences."
or
c.2) “We are not afraid to speak; we make many efforts trying to build well-balanced sentences."
My choice here would be c.2 “trying”, because “to try” sounds redundant after “many efforts”. In fact, even “trying” sounds a bit redundant and you could drop it altogether and go with:
d) “We are not afraid to speak; we make many efforts to build well-balanced sentences."
2) Although grammatically correct, “we make many efforts” sounds odd. Typically you’d find "efforts" as the subject, as in the phrase “many efforts are made”. I think it’s better as a) “we try hard to build...” or b) “we make many attempts to build... ”, depending on whether you mean quantity (your use of “many”) or quality (your use of “efforts”). You could also go with c) “many efforts are made to build...”. I believe a) sounds the most informal, b) is in the middle, and c) sounds the most formal.
3) “their/our”
a) If it is clear from the context that everyone is helping everyone else, then use “our” here:
“in order to improve our English.”
b) Otherwise, everyone is working (for the most part) independently, then use “their” (or “his or her”) here:
“in order to improve their English.”
“in order to improve his or her English.”
This is because "one's English" is typically a personal thing, and not considered part of the whole. We all study a language in class, but it's not really the class's language that is advanced; it's the individual's.
Also, prevailing (USA) thought is to eschew gender specific verbiage, if the intent is generic. This means that “in order to improve his English.” is avoided, though still found/heard.
4) “In order” is fine, but could be simplified as:
"Everyone in our group works hard to improve our English."
5) “sentences” was misspelled and there should be no space after the last period.
