So when these people come and are asking me in broken English what needs to be done, I have to take my time to make sure the job gets done?
No, you don’t have to do that. But then the job might not get done right, you'd end up contacting the landlord about that, and then they'd be back again to attempt to do right, which means even more interruption for you. But that's up to you to do. You may, of course, discuss your concerns with your landlord, and I would encourage you to do just that. But there is no law that imposes a requirement that the landlord himself must be there or that permits you to impose such a requirement. Any such requirement would need to be in the lease. Absent such a lease provision the landlord may simply hire the contractor and send in the contractor in by himself to do the work that is needed to be done.
And since you are not a woman home alone, I suppose you don't understand the need for a background check to make sure that who is coming into your home does not have a criminal record, or anything else that would show up being licensed or bonded.
First, understand that in Texas persons doing general repair work (handymen/handywomen) are not licensed by the state to begin with. The Texas Department of Licensing and Regulation (TDLR) regulates many professions and occupations in Texas, including those that involve particular aspects of construction, like electricians. You can find the list of regulated professions here: TDLR regulated professions. The TDLR does not regulate certain very highly regulated professions that instead have their own separate licensing bodies, including doctors, dentists, nurses, and most other medical professionals; attorneys; architects; and certified public accountants. But there is no separate regulatory agency for home contractors. So, if there is no requirement for a person to be licensed for the particular type of work being done (and most general repair other than electricial work does not require a license in Texas) then those people naturally aren’t going to have a license because there simply isn't one to get.
Second, most handymen are not going to be bonded, and bonding is no assurance that the person doing the work isn't going to be violent. No bonds are required by the state though some cities require what is known as a contractor's bond. Those bonds are protection against negligent work and fraud. It does not protect against everything. So being bonded is not quite the assurance you seem to believe it to be. Bonded or not, the vast majority of people doing home repair/construction work are not violent and there is no way to tell ahead time which person might be one of the few who are.
Finally, the statement you made was “Second, the guys he hires are not fluent in English and are not licensed
or bonded, so it makes me nervous to be here alone when they come in.” Whether you intended it or not, it comes across as a bit racially biased, implying that somehow guys whose first language is something other than English are somehow less trustworthy and more violent than those who are native English speakers. The fact is that race, national origin, or language has little to do with whether a person is likely to be violent.
I do not mean to suggest that your fears of being alone in your place when strangers are there doing work are completely unfounded. But as bonding and licensing are not required for most occupations/professions in Texas you cannot insist on that to get the comfort you are looking for. And insistence on a fluent English speaker is not only irrational in terms of safety, it also risks the landlord potentially violating federal and state laws against illegal discrimination.
Your concerns about how much supervision and input from you that these guys need is legitimate. You should not have to be the one telling them what to do. That's not your job and would be aggravating to be sure. That's the discussion to have with your landlord: ask him to get contractors who can do the needed work without having to pester you with questions about what they should be doing.