"I am writing to present my personal profile with a view to gaining employment within your company."
I'm afraid your sentence sounds unnatural, and "get inserted in the labor market" is completely unusable as a phrase.
"I am fully flexible with regards to location and hold a full driver's license."
Again, "full body mobility" is totally unsuitable - it suggests that you are a gymnast unfortunately.
Simply "subject to interview".
Please do not fall under the misapprehension that "formal letter" equates with "flowery phrases". It doesn't. Even more so than in normal conversation, simple sentences are best. A formal letter works best when it sounds curt and to the point. When you over-elaborate, not only do you sound false, but you run the risk of appearing absurd because you are stretching your vocabulary beyond your ability. Think twice before using idioms unless you are 110% confident that you know what they mean and that they fit in your sentence. After you've thought twice about it, avoid using them.
- For Teachers