Flying through Dublin, but changing airlines

I am flying Aer Lingus to London this summer for 2 months, but I am going through Dublin. I will then switch to a BMI flight (bought separately) to continue on to London. (It was cheaper and I was going to stay in Dublin a few days to visit friends before going to London, but that fell through.)

1- Will I have to go through customs, get my luggage and then come back through security all over again to switch flights?

2- If I do go through customs at Dublin, will I get the normal 30 day visit stamp? Will it matter that I am continuing on to London? I am staying 2 months (60 days) there with some side trips to Paris and maybe Spain during that time. When I come back to Dublin to check in for my flight home, will there be someone saying "hey! You only had 30 days and it's been 60!" since I likely won't go through customs again in London? As in, there may be no proof that I didn't just hang out in Ireland overstaying the 30 days visit.

I've never ever worried about this kind of thing before, but I want to make sure there are no problems either in Dublin getting to London or coming back home (which would seem unlikely). After all the reading of threads here on UKY I think I've confused and freaked myself out!

Oh, and despite being 35 and *really* just visiting friends, I still plan on bringing my teaching contract for next school year, bank statements showing I can afford my 60 day visit, and by then, year renewal on my lease. I anticipate these being unnecessary, but I'd rather be prepared!

Thanks for any advice/experience you can provide.

By leaving the UK and entering France or Spain, you'll have a Immigration stamp from those authorities showing you left Ireland. But from what I can gather, an Irish IO can land you for up to 90 days, so maybe those contracts etc will come in handy.

1- Will I have to go through customs, get my luggage and then come back through security all over again to switch flights?

If the two flights were bought separately, I'd say yes.  We did something similar when we went to the States for our wedding/honeymoon (bought a round trip ticket from Manchester to NYC, and then a separate round trip ticket from NYC to Houston because wedding was in Houston followed by an NYC honeymoon.)  I'm pretty certain we had to collect our bags and exit the "secure area" of the airport, only to turn right back around and check in for the next flight as if we had just come in off the street.

You will definitely go through immigration in Dublin though, there's no question about that.

When a person is given leave to enter for 6 months or less from anywhere within the CTA, that leave expires when they leave the CTA. 

What that boils down to is if you channel hop to Paris, the visa you got in Ireland will expire once you are enroute to the continent.  You will go through entry controls when you return and get a fresh visa good for 6 months.  If you then go to Spain, the same thing will happen.

The upside is that each time you go to the continent and return, you get a fresh 6 month visa.  You can do this indefinitely.  The downside is that each time you enter the UK, you start from square 1 with the duty IO.