What is the meaning of "There is None worthy of worship except Allah (SWT)?"

It means that there is no true deity worthy or worship except Allah (SWT) Alone.  Negating all false gods and affirming that Allah (SWT) is the Only True God.

What is the meaning of "Muhammd (SAW) is the Final Messenger of Allah (SWT)?"

It means total submission to him in whatever he (SAW) ordered, and avoiding whatever he (SAW) forbade and believing in all those matters that he (SAW) informed us about.

What are the conditions of the testimony of Faith?

There are seven conditions of the testimony of Faith (Shahada):

1. Knowledge which negates ignorance.

2. Certainty which negates doubt.

3. Sincerity and purity of intent which negates Shirk.

4. Truthfulness which negates hyposcrisy.

5. Love and devotion which negates disdain of Allah's (SWT) religion.

6. Submission which negates disobedience.

7. Acceptance which negates rejection or denial.