Does divorce take effect if the husband says to his wife, "Let's divorce, and be rid of this problem," but he does not intend thereby to effect a divorce, or if he says, "If you ask me for this, we will end what is between us," and she then asks for it?

Writing a divorce (talaq) message on a mobile phone without uttering it verbally is considered a metaphorical expression (kinayah), and thus, divorce does not occur without the intention (niyyah). The divorce pronouncements mentioned in the question, being in the present tense, can be interpreted as a promise (wa'd), which is also a metaphorical expression (kinayah) and does not result in divorce without intention. The husband's statement regarding his intention when uttering these metaphorical expressions is accepted, as he is the most knowledgeable about his own intention. Therefore, as long as the husband states that he did not intend divorce with any of these phrases, his divorce has not occurred, and he is not required to pay expiation for an oath (kaffarat yameen), unless he swore by Allah that he would divorce and then did not divorce, in which case he must pay expiation for an oath.