Is this considered breaking in my phone or stalking?

No, if the phone was left in a place that a family member could access it there is not enough to involve the authorities

Will a verbal agreement hold up in court.

It would seem the agreement for the 50 50 split can be enforced since both sides agree that was the verbal agreement, Beyond, that, it cannot be...

Will my mother have to pay her lawyer before she can hire another one?

You simply have not got enough information here. For all you know, the lawyer has put in a lot of work, but remember, YOU ARE NOT THE CLIENT,

Can I still Sue my ex boyfriend?

If you have solid evidence that he did it and the amount of property damages, yes you may still bring a civil lawsuit

What should I do if I am being sued for breach of non competitive contract in La. ?

You had better hire an attorney to defend yourself because you now know you should have had legal counsel about what you signed and what it said...

Will the court dismiss contempt charges prior to the hearing; therefore, prempting the need for said hearing?

No court administrator can legally enter any order of court without the judge making the decision

Should I sue to get my $3,000 security deposit back?

Yes you should sue in my opinion, yes,

Other than your suspicion you have no admissible evidence about who is smoking to prevail in any court case

Do i have to show up on the specified date or can i ignore this docket?

Based on your description you have this docket entry via court order to safe families.

You will not be able to sue successfully for things that were "visible and noticed"