A few disjointed thoughts, subject to the disclaimer that I've not worked in housing benefits for quite a few years and am getting more out of touch.
Trying to tackle this one bit at a time -
Your tenancy - there has been some publicity in some areas about "illegal sub-letting" of social housing. This is about cases where a social tenant lets the whole place to AN Other and goes and lives somewhere else. That is generally a breach of a tenancy agreement. That is NOT what you're talking about here.
Most social tenancies allow you to 'sub let' (same term but different meaning) a spare room to a lodger (and some politicians / councils have encouraged people to do this to avoid being bedroom taxed.) You'd need to look at what your tenancy agreement actually says to see about this - you may need to seek permission or inform them, but as long as your place wouldn't become 'overcrowded' as a result, I suspect it's not going to be an issue. And having said that, if it's a family member and not a commercial agreement, it may not count as sub-letting.
And I'd have thought friends / relatives could come and stay with you for a short while without you needing to tell anyone - I'm not sure how long would count as "a short while" though, and if they didn't have a permanent address anywhere else it might be dubious.
The council can't increase the rent, as it's done on a per property basis. There is some speculation at the moment about making 'high earners' pay higher rents, but this isn't even draft law yet, it's likely only to mean people on fairly high wages (£ 40K a year is being talked about) and it may or may not be retrospective to existing tenancies.
If you have a secure tenancy, they can't evict you unless you do something that's a fairly serious breach of your tenancy agreement.
Are you currently getting housing benefit? If so, then this arrangement will affect your housing benefit entitlement (and could reduce the amount of HB you get, hence you may have to pay more rent) - this would be a 'non dependent deduction' from your HB - more
here (from Shelter) - but on the other hand, I think this means you'd not get 'bedroom taxed'
Likewise, it may affect the council tax benefit / council tax reduction you get - as well of course as the 25% single person discount off your council tax.
As with all things like this, it would be better to tell the housing benefit / council tax benefit people (may or may not be the same office at your council) as soon as it happens, to declare a 'change of circumstances' rather than wait for them to catch up with you - this can lead to all sorts of complications.
As regards ESA (ESA is run by the DWP not the local council) it may affect you if you're getting income related ESA - although you should make it clear that you're not charging a commercial rent, just expecting them to pay a share of bills and make up the non dependent deductions in your housing benefit etc. That may or may not count as "income" for ESA purposes.
Gut feeling is you should not end up overall worse off as a result of this (taking in to account HB, ESA and the contribution that offspring makes) although not sure you'll end up much better off.
If you're getting contributions based ESA, then this shouldn't make any difference to that, but it may be worth letting the ESA people know in any case.
You don't need to worry about income tax implications - you are allowed to make up to £4,250 per year from renting a furnished room in the home you live in before the tax-man wants to know.
It might be worth having a play with the benefits calculator
here (this is independent of DWP / councils and you don't give any personally identifying info) although not sure it can cope with non-dependents...
Best of luck, try and take it one chunk at a time, and talk to Shelter or CAB if you have problems.