The position of already in a sentence is pretty interchangeable, in terms of spoken English. All four of your example sentences are commonly spoken uses of already and if there were any implications, i.e. surprise at the amount of time, etc., then they would be clarified in tone of voice or surrounding context. I will say that placing already at the end of the sentence is slightly more informal and in speaking the tone of voice you use will be especially important so as to not seem rude or dismissive. However, using the proper tone of voice either way of using already can be and is usually used in speaking. Hope this is helpful:)

Hi! Yes, you're correct. Adverbs usually go attached to a verb, for that's what the adverb is modyfing. Depending on the position, it may sound stronger or in a different way, which also depends on the hearer. I already miss you. This may suggest that, from this soon, you miss someone very much. You said "I ALREADY", as if it was unbelievable. I miss you already. This can give a more relaxed idea of how much you miss them. You still do, but it's not as strong as the previous one. I hope that helps! Otherwise I'll explain in a different way!

We usually put already in the normal mid position for adverbs (between the subject and the main verb, or after the modal verb or first auxiliary verb, or after beas a main verb) We can use already at the end of a sentence for greater emphasis or to show greater surprise. This is especially common in informal speaking. Então é mais formal usar "already" antes do verbo. Pra mostrar mais surpresa você lhe utiliza no final ou quando tá falando informalmente. Espero que seja de ajuda para você.

This link might help you to clear up your doubts: https://dictionary.cambridge.org/grammar/british-grammar/adverbs-of-time-and-frequency/already But summarising, placing already at the end of the sentence emphasise the time expression (it could sound a little informal) and putting in it in between the subject and verb is just the usual way of doing it. Greetings!