Is a handwritten will and last testament considered legal in a court of law?

It's called a holographic Will. It has to be written completely in the Decedent's handwriting and signed, but it does not have to be notarized.

In Texas is it necessary to find at least two (2) people who are not beneficiaries under the terms of the Will and can attest under oath that they know that it is the Decedent's handwriting.

Typically, these estates require an Administrator who must post bond as most people don't know how to properly phrase it so that they can have an Executor/trix acting without bond.

ALL STATES HAVE DIFFERENT LAWS. NEVER TAKE LEGAL ADVICE FROM A STRANGER ON THE INTERNET. ALWAYS CONTACT A LOCAL ATTORNEY TO VERIFY THE LAWS OF YOUR STATE.

as long as it is notarized

Anything written, signed, and notarized could be considered legal, depending on the assests of the ward or the estate if it is technical, disputed by other beneficiaries it could get tricky. Small estates usually wont need a trustee or conservatorship, talk to an estate planning group

it is as long as the signature is affixed on it

As long as it is witnessed and notarized it should be good to go.

If it is just an older will that happened to be handwritten than you are fine, but if you are writing a new will than it should be typed as the courts frown upon handwritten paperwork.

Yes, It is HIGHLY state dependent,
BUT in general following rules will apply:
* There must be evidence that the testator actually created the will, which can be proved through the use of witnesses, handwriting experts, or other methods.
* The testator must have had the intellectual capacity to write the will, although there is a presumption that a testator had such capacity unless there is evidence to the contrary.
* The testator must be expressing a wish to direct the distribution of his estate to beneficiaries.