figure out,是自己想出来的某个问题,某个想法.例如:
After several days,I still can't figure it out.【经过几天了,我还是想不出来】
catch on,是针对对方的问题,或者某个提示,理解了对方说的话.例如:
Sorry,I don't catch on your joke.【抱歉,你说的笑话我没听懂.】
get across,通常代表的意义,是被动的.例如:
Although I explained,I couldn't get my meaning across.【虽然我解释了,我还是不被理解】
至于词性,是没有啥区别,都是一个动词加上一个副词的组合.