The offeror is "master of the offer" including the manner in which the contract may be accepted. Where the offeror specifies that acceptance may be by specific conduct, the question becomes "whether the offeror, acting reasonably, would understand that the offeree was assenting to the terms proposed." This is not implicit acceptance; this is acceptance by conduct. This is an objective inquiry focusing on how the actions would be understood to a reasonable observer, not an inquiry into the actual states of mind of the offeror or offeree.
It is a question of fact, on a consideration of all the circumstances, whether the conduct of the offeree constitutes an acceptance of the offer. It is open to the offeror to specify the manner in which the offer is to be accepted. Where the offeror does so, this is a significant factor to be taken into account in determining whether or not the conduct of the offeree constitutes acceptance. The conduct of the offeree must be considered in the light of the acceptance provisions specified in the offer.
(Hill v. Develcon Electronics Ltd. (No. 1), 1991 CanLII 7744 (SK KB))
As is the case where acceptance is intended to be, or is appropriately indicated by some statement by the offeree, whether oral or in writing, the nature of acceptance by conduct depends upon the requirements, if any, stipulated by the offeror. In the absence of any special act or conduct prescribed by the offeror, acceptance may be inferred from the offeror’s [sic: should read "offeree's"]1 conduct. Yet such conduct must indicate: (a) that the act in question was performed with a view to acceptance of the offer, and not from some other motive or for some other reason; and (b) that it was intended to be acceptance of the offer in question. In such cases the question is whether a reasonable man would interpret the offeree’s conduct as an acceptance of the offer.
(Fridman, The Law of Contract in Canada, 4th ed. (1995), p. 56)
A person is not held to terms that they could not have known at the time of the acceptance. See Thornton v. Shoe Lane Parking Ltd., [1970] EWCA Civ 2.
Some onerous or unusual terms are treated with particular skepticism. Unexpected exclusion-of-liability clauses, for example, have been held not to be enforceable unless the offeror takes reasonable steps to ensure the offeree is notified of such clauses prior to their acceptance. See the discussion at Apps v. Grouse Mountain Resorts Ltd., 2019 BCSC 855 at paragraphs 22-31.
How the above law would apply to any of the circumstances you describe is for a finder of fact, and you are as well placed as any of us to go through that exercise.
For a critique of the common-law position, see Margaret Jane Radin, Boilerplate. She agrees that the above is the state of the law, but discusses the fiction of agreement and criticizes such contracts as "rights deletion schemes" that create "alternative legal universes."
1. This was likely meant to say "offeree's conduct." At least two courts have indicated this was an error in the original: e.g. 1; e.g. 2.
