1) Absolutely, it's possible! The sentence you gave is a good example. A few other examples off the top of my head could be:
- Voy a buscar una tienda que venda cinturones cuando ella llegue. (I'll look for a store that sells belts when she gets here.)
- Mañana buscaré un trabajo que pague mejor, a menos que el que tengo me dé un bonus grande. (Tomorrow I'll look for a job that pays better, unless the one I have gives me a big bonus.)
- Cuando cumpla los 18 años, me casaré con el primer hombre que me encuentre bonita. (When I turn 18, I'll marry the first guy who thinks I'm pretty.)
2) and 3) No. You must understand that while the subjunctive mood is complicated for native English speakers to learn, it is no more complicated than any other mood or verb tense for Spanish speakers. Removing subjunctive verbs does not simplify sentences; it changes their meaning (sometimes subtly, sometimes drastically). For example, consider the following sentences:
A. Voy de compras cuando llego al centro.
B. Voy de compras cuando llegue al centro.
Sentence A communicates a habit or repeated action. It implies that you have arrived at the city center in the past, and you normally go shopping when you arrive. Sentence B implies a hypothetical/future situation: you haven't gotten to the city center yet, but you're on your way, and you plan to go shopping when you get there.
The reality is that native speakers of Spanish cannot consciously distinguish between subjuntive and indicative any better than your average native English speaker can distinguish between the gerund and the present progressive. Your third question is kind of like asking, "Do English speakers try to simplify their sentences by using regular past-tense verbs instead of irregular past-tense verbs?" Of course we don't. We use whichever verb/tense/mood/expression best communicates our meaning, and most of us are not able to explain the grammar we're using!
As an English speaker learning Spanish, my advice is to try to think of the subjunctive not as a complication of "simpler" grammatical constructions, but as an integral part of the Spanish language that helps you communicate specifically and accurately. It is very challenging, but you should be using it a lot! A Spanish grammar teacher (and native speaker) once told me that it's rare for 30 seconds go by in a conversation without the subjunctive making an appearance at least once.