Learn English – start a sentence with the word maybe

Run to me, I get you to some place to hide.

This sentence starts off just fine. Verbs that command to someone to do something have the "implied you" as the subject. This is called an imperative sentence. As it says at one website:

IMPERATIVE
An imperative sentence gives a command. For example: "Shut up and kiss me."
Note that an imperative sentence does not require a subject; the pronoun you is implied.

That said, the sentence could still be improved; "someplace" is one word, and the second half of the sentence should include the word "will":

Run to me, I'll get you to someplace to hide.

Observed the experiments, I learned that "Failure is a mother of Success".

This sentence has problems. The main verb here is learned, not observed. You could fix this in one of two ways:

Fix No. 1: Start the sentence with a prepostional phrase

This would require you to change the word "observed" to its gerund form:

By observing the experiments, I learned that "Failure is a mother of Success".

Fix No. 2: Start the sentence with the subject and use a conjunction

This could be accomplished by using a compound verb:

I observed the experiments and learned that "Failure is a mother of Success".

or by making it a compound sentence:

I observed the experiments, and I learned that "Failure is a mother of Success".

Neither one has a higher chance. See possibly and maybe, and also perhaps. Also in Oxford (maybe).

Will you go to the new movie Friday?

perhaps
maybe
possibly

Possibly seems a bit more formal.

Also while you can say

I'll possibly go

saying

I'll perhaps go

is a bit weird, while

I'll maybe go

sounds really informal, if not uncouth.