You already own a bicycle.
The correct sentence is He is allowed to do it on his own.
I can only guess at what you are trying to say, but I guess that this sentence should have been, understand it in your own home. You don't have to go to school to learn about this; you can understand it in your own home.
"The dog has its own collar" is grammatically correct. Many people mistakenly use "it's" in this kind of sentence, but that is the contraction for "it is," not the possessive form of "it."
"Becky wanted a bicycle badly" is the independent clause. It can stand on its own. The rest of the sentence cannot, so it is a dependent clause.
Either "You went in your own way" or You went on your own way" could be correct. The first sentence would imply individuality in the manner of going, but the second would imply individuality in the route selected. For example, "Everyone else went by train, but you went in your own way by bicycle" and "Everyone else took the main road, but you went on your own way by a barely marked trail."
Do you own a computer? Grammatically it makes sense as a question. You do own a computer would be a suitable answer.
No. This is a clause that cannot stand on its own. It is not a complete sentence. A sentence needs a subject and a verb.
I'd like to congratulate you on already answering your own question.
Most bicycle owners maintain their own bicycle. But, a bicycle shop may be willing to maintain a bicycle, if you ask.
Yes, I can: I didn't get a ride, I got here on my own.
Who, what where why and how can be used to start an interrogative sentence, and can be a sentence on their own as declaratives understood , or as exclamatories. The word 'when' is also used to introduce dependent clauses, such as the famous clause "when in the course of human events" or the more pedestrian "when you go to the store." Either of these, when followed by a comma and an independent clause, could start a sentence.
No