I very much enjoyed your paragraph and the portrait of your family! If you'd like to revise with a focus on only grammatical issues (as opposed to the questions of style and personal taste that mwestwood addresses above), here's where I would start:
There's an article missing in the line "She was a single mom for long time"—the phrase is usually "for a long time." (Articles are tough.)
The sentence "My younger brother is studying in grade 10 at Overfelt high school" sounds grammatically correct to me, but "studying in grade 10" is a phrase that I've heard less often. The more typical way to express that idea might be: "My younger brother is in 10th grade at Overfelt High School." (Also, in the name of the high school, the words "high school" are usually capitalized—so "I go to high school" is just fine, but if you say "I go to Overfelt High School" it has to be capitalized as part of the name "Overfelt High School.")
"He always walks or takes the bus to school because he doesn't has driver" is really close! "Has" should reflect the auxiliary verb "does" (or here "doesn't") next to it: "He always walks or takes the bus to school because he doesn't have driver." "Driver" also needs an article: "he doesn't have a driver."
"He always jokes and tells something funny" is also really close! The only thing is that "tell" usually takes a direct object (meaning you have to tell someone). So how about: "He always jokes and says something funny"? Or maybe "He always jokes and tells me funny things"?
"He is a dynamic and talkative" gives me a great picture of your brother's personality! The only grammar problem here is the article (again, articles are tough). "Dynamic" is an adjective (not a noun) so it doesn't require an article. You can just say, "He is dynamic and talkative."
I understand the phrase "we always spend a good time together" with no problems! I think the more typical phrase, though, is "we always have a good time together."
Those are the only grammatical questions I had! Your family sounds wonderful. Best of luck with your studies!
For the most part, your grammatical constructions are correct. In the 4th sentence, however, you will want to change the verb took to has taken (present Perfect tense, meaning the action started in the past and continues into the present).
This autobiographical paragraph needs revision more than it needs grammatical correction. Combining sentences will give your writing a better "flow" and using connecting words (see the ones in bold) will greatly aid the transition of ideas. Perhaps, too, some sentences should be placed in a different part of the paragraph. Here is a suggested revision:
My family is a small one with only three members: my mother, my brother, and I. My mother is a great woman who has always taken very good care of my brother and me. Unfortunately, she is currently unemployed, but we feel secure with her at home when we are. Every morning she fixes breakfast for us, and then my brother, who is in tenth grade, either walks or rides the bus to Overfelt High School. On the other hand, I work at Micro Lamba Wireless Company, but when I am not working I study English at San Jose College. Not only do my brother and I differ in age and occupation, but we are unlike in personality. While I am shy and quiet, my brother is very amusing because he is always telling jokes or saying something funny. In brief, we may be just a small family, but we always spend a good time together since our mother is so caring and my brother so amusing.
Note: Check the links below for transitional words and other ideas.