I'll tackle as much as I can before dinner...
1) Assuming that you and the other party are in fundamentally similar jurisdictions, contracts can be formed in lots of ways. For sales contracts, the basic terms are the parties and the price. A lot of "default" conditions can be attributed to a contract based on what is reasonable or ordinary in a given market. If the standard terms in the soybean market are, say, "net 30", and you and the other party are both soybean merchants, then you had better be able to pay for your shipment of soybeans 30 days after delivery. Domains are not soybeans, and unless you had some other understanding before striking a deal, people generally expect you to be able to pay cash on the barrelhead. Your question is framed a bit oddly since you say, "I can only pay someone two weeks after buying a domain name".... that sort of begs the question of whether you did, indeed, "buy" the domain name. When did you "tell them" you couldn't pay right away? Before you agreed to a price or after?
There is also the issue of how one might objectively understand the communications involved. Did they reasonably perceive you as saying "If I come up with $X two weeks from now, will you sell me the domain name?" They can say "yes" to that, but you do not have a valid contract to buy the domain name in two weeks. It would be different if you said, "Will you take $50 now in order to commit to selling the domain name to me two weeks from now for $X?" In that case, what you have is an "option contract" - i.e. a contract-within-a-contract where they have agreed to hold the price for you for a period of two weeks.
Finally, the deal may fall into the "statute of frauds" within one of the respective jurisdictions. Most US states, for example, will set a dollar limit on the value of contracts that can be enforced without a signed writing enforcible against the party against whom the contract is being asserted. If the value of the contract exceeds the limit of the relevant statute of frauds, then you would need what people more usually think of as a formal, signed contract.
2) "Ever"? No. Each US state has its own set of rules, all of which generally follow similar patterns derived from the ABA Model Code of Professional Conduct and the ABA Model Rules. Some of the state-by-state differences are interesting, and I highly commend the website www.legalethics.com, which provides an online directory of state conduct codes and disciplinary rules (click on the "ethics" link at left, and then pick your state from the pull-down menu. If there is a unifying principle here, it is that if the subsequent representation would necessarily rely upon privileged information gained during the prior representation, then there is absolutely no way that the lawyer should take on the subsequent representation. The principle is generally stated in transactional or "subject matter" terms. For example, if I represent Able during the negotiation and drafting of a contract for the sale of a horse to Mr. Baker, then I cannot later represent Baker in an action to enforce the contract against Able. If, however, next year Mr. Charlie comes to me with a contract under which Mr. Able sold him a cow, and there is nothing about the horse deal that would provide me with an "edge" in enforcement of the cow contract, then Mr. Charlie may hire me to enforce the cow contract against Mr. Able. However, I would inform Mr. Charlie of the circumstances of my prior unrelated representation of Mr. Able. Personally, however, I'd be inclined to simply decline the representation, because even close adherence to the rules is sometimes too close to avoid someone raising a question.
So, I'll let the relevant Pennsylvania code section and commentary speak for itself:
Rule 1.9 Conflict of Interest: Former Client
A lawyer who has formerly represented a client in a matter shall not thereafter:
(a) represent another person in the same or a substantially related matter in which that person's interests are materially adverse to the interests of the former client unless the former client consents after a full disclosure of the circumstances and consultation ; or
(b) use information relating to the representation to the disadvantage of the former client except as Rule 1.6 would permit with respect to a client or when the information has become generally known .
 After termination of a client-lawyer relationship, a lawyer may not represent another client except in conformity with this Rule. The principles in Rule 1.7 determine whether the interests of the present and former client are adverse. Thus, a lawyer could not properly seek to rescind on behalf of a new client a contract drafted on behalf of the former client. So also a lawyer who has prosecuted an accused person could not properly represent the accused in a subsequent civil action against the government concerning the same transaction.
 The scope of a "matter" for purposes of Rule 1.9(a) may depend on the facts of a particular situation or transaction. The lawyer's involvement in a matter can also be a question of degree. When a lawyer has been directly involved in a specific transaction, subsequent representation of other clients with materially adverse interests clearly is prohibited. On the other hand, a lawyer who recurrently handled a type of problem for a former client is not precluded from later representing another client in a wholly distinct problem of that type even though the subsequent representation involves a position adverse to the prior client. Similar considerations can apply to the reassignment of military lawyers between defense and prosecution functions within the same military jurisdiction. The underlying question is whether the lawyer was so involved in the matter that the subsequent representation can be justly regarded as a changing of sides in the matter in question.
 Information acquired by the lawyer in the course of representing a client may not subsequently be used by the lawyer to the disadvantage of the client. However, the fact that a lawyer has once served a client does not preclude the lawyer from using generally known information about that client when later representing another client.
 Disqualification from subsequent representation is for the protection of clients and can be waived by them. A waiver is effective only if there is disclosure of the circumstances, including the lawyer's intended role in behalf of the new client.