Can you get any kind of residence in UK through a gay civil union or marriage or such kind?
Would I be able to get residence in England if I get married to my boyfriend (he is British)?
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The UK recognises same-sex marriages - as marriages in England, Wales and Scotland or as civil partnerships (with the same rights as a marriage but without the name) in Northern Ireland.
That means that the same rules apply to you as to anyone else married to a British Citizen.
Your own nationality is not relevant to this process (except that if you're an EEA citizen you have resident rights in the UK and you don't need to bother).
The general eligibility rules are here on the UK government website - your partner has to have an annual income of £18,600 a year (more if you have children) to be able to support you (your own income doesn't count); you have to pass an English language test unless you're a national of an English speaking country (e.g. USA) or you have a bachelor's degree (or a higher qualification) that was taught through the medium of the English language; depending on which country you're coming from, you may need a tuberculosis test. You have to apply and receive the visa before you enter the UK, and you need to renew it annually.
Once you've been in the UK five years, you can then apply for indefinite leave to remain (ILR: the UK equivalent of the US green card); you'd have to pass the "Life in the UK Test" (a basic civics test) and prove that you (now jointly) still have an income of £18,600 a year (more if you have children). ILR means you don't have to renew your visa every year, and you become eligible for some social security (e.g. disability and unemployment benefits). With ILR, you could only be deported for becoming a persona non grata (ie for committing a crime, or for being reasonably suspected of being a terrorist, a spy or someone trying to overthrow the British government), whereas on a spousal visa you can be deported for not filing visa renewal forms on time.
You would then become eligible for naturalisation as a British Citizen three years after the grant of ILR, so long as you're still married, so eight years after you arrived. British Citizenship doesn't make much difference from ILR as long as you stay in the UK, but it does entitle you to full freedom of movement within the EEA, so you can live or work anywhere in the EEA (nearly all of Europe) without need for visa or work permit.