Partner of short term student, applied for Luxembourg citizenship - should she mention it in the landing interview at the UK border (visitor visa)?

I'm in a situation with my girlfriend and generic advice online is not helping. I was wondering if you could help me regarding what would be useful at the border:

Main info:

• I will be in the UK midlands with a short term study visa (6 months) from October 2019 to April 2020. This is genuine. I have to, and will, come back to my country after the period is over.
• She will stay in the UK from November until March (4 months). This is also genuine. She will also come back (she already has the return plane ticket, etc).
• We're both from Brazil.

The prickly:

• Her work contract is up in November, so she won't have a job by the time she goes. Even though that's the source of the savings she will spend in the UK, they might find she's unemployed if they ask how come she's able to spend 4 months away from work, so we're thinking it's not wise to hide the fact she's unemployed. She's not studying either.
• Our best plan so far is to have her inform tourism / visiting a friend as her purpose. She will have an invitation letter (from an acquaintance - my colleague, who's letting the house for me/us). My colleague rents his own mother's house, so to simplify (and bypass the whole "the landlord also has to agree" thing) we'll just say my colleague will host her in his mother's house.
• We're planning on saying she's yet to plan her itinerary as there will be plenty of time to do so, but that she's aiming at improving her english (through regular usage with locals) and getting to know British culture by visiting several cities within these months. Well, this isn't even an plan, really; it's all true.
• We're also planning on saying her father will be sponsoring her trip. He's a retired public servant and has enough money, and we'd have his financial documents to back it up. We're thinking about this because they might suspect her in case she just plans on spending most of her savings on a trip, so we thought adding this sponsor might make the claim stronger.

The questions:

1. Should she mention ME at all? Would that make it EASIER? ("well, he has to come back so I guess she will too, and that explains why she's here for so long") Or would it make it HARDER? ("so her boyfriend's already here? She's not planning to leave! And neither is he! It's all a scheme!!!!!")
2. She's also applied for citizenship in Luxembourg - she has to go there to complete the process. She's planning on doing that while she's in the UK. Should she mention that at all? Would that make things easier or harder?
3. How much money is she expected to bring to spend 4 months in the UK? (Considering she won't spend anything with accommodation). I know there isn't a minimum, and that bank statements are asked to ascertain more than that. But since it's a long period of time - would ~3000 £ be enough, or it would raise eyebrows?

We don't intend on lying, we're just trying to figure out what information should be given upfront / even if not asked specifically, that is, if said information could help at all or if we should be prepared for it to be a problem.