It depends on what kind of court this lawsuit was filed in. If it was filed in Texas District or County Court, the plaintiff must allege in paragraph 1 of the petition which level of discovery control applies to the lawsuit. That will set the initial limits on what discovery you can do. You do not file most discovery or discovery requests with the court. You instead make your requests of the other party (the landlord) directly. Rule 191.4(b) of the Texas Rules Civil Procedure tell you which discovery matters to file with the court:
(b)Discovery materials to be filed. The following discovery materials must be filed
(1)discovery requests, deposition notices, and subpoenas required to be served on nonparties;
(2)motions and responses to motions pertaining to discovery matters; and
(3)agreements concerning discovery matters, to the extent necessary to comply with Rule 11
Rule 191.4(a) tells you specifically NOT to file with the court the following:
(a)Discovery materials not to be filed. The following discovery materials must not be filed:
(1)discovery requests, deposition notices, and subpoenas required to be served only on parties;
(2)responses and objections to discovery requests and deposition notices, regardless on whom the requests or notices were served;
(3)documents and tangible things produced in discovery; and
(4)statements prepared in compliance with Rule 193.3(b) or (d)
So, if the case is in district or county court my guess is that the court has not responded to what you filed because you weren’t supposed to file it in the first place. There are time limits for discovery, and with trial set for September 12 it may be too late to begin discovery.
If the case is in Justice Court, then you do need to first file a request with the judge to conduct discovery, and the judge will only approve it to the extent the judge finds discovery “reasonable and necessary.” See Rule 500.9(a). So in that court discovery is not the norm. I don’t know why the judge has not ruled on your motion if it is in Justice Court, but it may simply be that the judge isn’t inclined to approve the motion anyway. In any event, in Justice Court you cannot proceed with discovery until the court approves it.
There does not appear to be one. You’ll have to prepare your own motion for it unless your local court has one. The forms approved for state wide use are located here: Texas Court Forms
The court may not approve the request, and appearing by phone can be a disadvantage to you. It is always preferable to have the parties there in person when possible. If the case is tried to a jury in particular having a party appear by phone is really not very workable. Even tried to a judge it presents some problems. The judge cannot see you, and seeing you and your body language, facial expressions, etc are important for determining credibility. You also are not there to be able to submit any documents, etc., into evidence. It's worth asking for if you really need to do it by phone but just understand the limitations that it presents.
If you are going to represent yourself, you need to know the rules of procedure that apply to the court in which the case is being tried. So get the Texas Rules of Civil Procedure and the Rules of Evidence. You'll find those here: Texas Court Rules

