All three of these points are rather weak and easily countered, but the last one is probably the weakest of the three, and is the only one I'll discuss here.
The basis for the argument is the Greek preposition eis which, in the relevant passages we'll examine, is translated as out of and into. However, it can also be translated as to, upon, unto, towards, for, and among.
The most quoted passage is that of Jesus' baptism, another famous 3:16 verse:
And Jesus, when he was baptized, went up straightway out of the water: and, lo, the heavens were opened unto him, and he saw the Spirit of God descending like a dove, and lighting upon him: (Matt 3:16, KJV)Here the argument goes that if Jesus came "out of" the water, then he must have been immersed. Obviously that is not the case: if one is waist deep with a dry head one can still come up out of the water by walking to the shore. This passage is, at most, suggestive of immersion. It does not require it.
However, the death blow to this argument (not the death blow to the case for immersion, just the death blow for using such passages to prove that it is the only legitimate mode) comes from the case of the Ethiopian eunuch. There we read:
36As they traveled along the road, they came to some water and the eunuch said, "Look, here is water. Why shouldn't I be baptized?" 38And he gave orders to stop the chariot. Then both Philip and the eunuch went down into the water and Philip baptized him. 39When they came up out of the water, the Spirit of the Lord suddenly took Philip away, and the eunuch did not see him again, but went on his way rejoicing. (Acts 8:36-39, NIV†)The problem here for Baptists is that whatever was described for the Ethiopian in relation to the water must also apply to Philip. They both went "into" the water. They both came "up out of" the water. If such language, the same as used in describing Jesus' baptism, demands immersion—then we must conclude that the baptizer (Philip) was also immersed. I know of no Baptist church that requires the pastor to be immersed when administering the ordinance.
† The observant will note there is no verse 37. It was not left out.