Can someone explain these in basic english to me

The snappily-titled Civil Partnership and Certain Rights and Obligations of Cohabitants Act 2010 Part 15 does confer - as the title of the Act suggests - certain rights and obligations on qualifying cohabiting couples. And it does provide, in s. 202, that a cohabiting couple can, on certain conditions, "enter into a cohabitants’ agreement to provide for financial matters during the relationship or when the relationship ends, on death or otherwise". And their agreement can have effect "notwithstanding any enactment or rule of law" — i.e. it can prevail over the standard rights and obligations imposed by Pt 15.

And the extract posted in the OP looks like an extract from a model cohabitants' agreement — the reference to s. 194 tells me that, since s. 194 is the provision giving cohabitants a right to apply for provision out of one another's estates.

(Whether it's a good model agreement, or whether it's a rehashed version of a standard separation agreement I cannot say. I've only seen the one clause. As already mentioned, I don't think the drafting would win any plain language awards.)

You should be aware — no doubt your solicitor has made you aware — that cohabitants' agreements are not absolute. A court can vary one or set it aside "where its enforceability would cause serious injustice".

I mention this because its clear that there is considerable economic disparity between the two of you. You own property and a pension which, you might reasonably hope, will appreciate in value as the years go by; she owns only a car which in a few years will be worthless. It's clear that she is the economically vulnerable partner, with potentially much to lose if your relationship endures for some time, and then ends. Much depends on what happens between now and then — does she make choices or life changes in reliance on the relationship that diminish her earnings or impair her capacity to build wealth? — but, when you say that you want to "make sure" that she cannot claim your property or pension, you need to be aware that you cannot make absolutely sure of this. The cohabitation agreement may be varied or set aside.

That's not to say that it's useless. The longer your cohabitation continues, the more likely it is that facts will change, developments will occur, etc that make its terms inappropriate to your circumstances, and the greater the risk that, when the time comes, it will not be enforced. But if your relationship ends after a relatively short time when both your circumstances are much as they are now then there is very little chance that it would not be enforced. And, of course, if after a couple of years you transition from cohabitants to spouses, your agreement has no relevance after that. (I note that you say the parties might possibly be related in the future, which I take to mean that you might marry.)

So, as to the draft provisions of cl. 13:

You need to think what should happen in the event that you die while this relationship continues. (I'm assuming here that you will both be living in the house that belongs to you alone.) Should your partner have to leave your house so that it can be sold and the proceeds distributed to your brothers and sisters, or other family members? Should your house be left to her? Should she have a lifetime right of residence in the house, with eventual sale when she leaves or dies for the benefit of your family? Something else?

And you could raise similar, if less pointed, questions in relation to the rest of your property.

Different couples will answer these questions differently, depending on their circumstances and on the way they see their relationship. An older couple, both of whom have had previous relationships and perhaps have children from those relationships, and both of whom already have some wealth, might decide to keep their estates entirely separate, each leaving all their property to their existing family. Or they might decide to do that, except for the home they share, which will go to the survivor of them. Or some variation that. Whereas a couple with no existing family commitments or obligations, and perhaps not much wealth between them, might decide the opposite; they will each make a will leaving everything to the other, which they will agree not to revoke or alter unless the relationship ends. Or, they might agree the opposite, if they both see their relationship as relatively casual or provisional or transient.

So, this is something you need to think about, and then its a conversation you and your partner need to have. What goes into cl. 13 will depend on the outcome of that conversation.

Draft para (a) is suggested for the couple who are going to keep their property and financial affairs entirely separate and who agree to leave nothing to each other.

Draft para (b) might be appropriate for a couple who do want to look after one another in the event that one of them dies, but who also have obligations to existing families.

Draft para (c) is not really alternative to (a) or (b), but might be something you would want in addition. Under s. 194 of the 2010 Act, if one cohabitant dies, the other can apply to court to get some part of the estate. If the court thinks that the deceased cohabitant hasn't made proper provision for the survivor and that this is unjust, it can award whatever it thinks appropriate. Draft para (c) would rule out a court application of this kind, based on the fact that the couple will make what they agree to be appropriate provision for one another, as reflected in para (a) or (b) or some variation of them.

Draft para (d) would be an exception to draft para (c) — "you can't apply for a share of my estate, but you can apply for temporary maintenance for a period after my death; e.g. a right to live in the house for 12 months, and to get a continuation for 12 months of whatever regular financial support you were getting from me before my death". That's the kind of practical arrangement that might need to be made when one partner dies unexpectedly.