Is there a breach of contract?

You can sue for breach of contract, but the contract would have to be reviewed to fully advise you.

What should i do? i am not paid the rate that i signed the contract for.

You can sue for breach of contract, but the contract would have to be reviewed to fully advise you.

Can my landlord request a copy of a lease I signed with someone else?

No, you have no obligation to provide your new lease to your LL.

What at the very least or at the very minimum would constitute a "written" agreement between two parties?

Depending on the exact verbiage of the emails, yes, they could constitute a written contract.

I need to establish a business in los Angeles and I don't know California rules, what kinda attorney I have to hire?

A business attorney can assist you. A full consultation would be necessary to properly advise you.

Social media networking website for high school students

Privacy policy, terms of use, terms of service, perhaps other disclaimers. A business attorney can help with this.

If you are on modified duty and you can .only lift 5-10 pounds and the employer tell you to lift over 10 pounds or more.

You may have a claim for your employer failing to reasonably accommodate you.

How does a partnership sign a lease?

The partnership would just sign as the entity. For example, ABC Partners, LLP.

Is a Letter of Intent to Perform sufficient to make subsequent representations or guarantees to third parties?

You may have some valid claims, but a full consultation would be necessary, including review of all documents involved.

You may have claims for unpaid overtime, and damages for meal periods and rest breaks that weren't provided. A full consultation would be...