1) Larger cog rear, smaller chainring front. You didn't say whether it has a freewheel or a cassette, but larger versions are available in either, up to about 32-34 teeth. If your RD accommodates the 28, it will probably handle 32, at least. Can't say whether that gets you more or less than you could get with a chainring switch, because we'd need the particulars on your cranks to know that.
2) Probably not. You don't mention what crankset it has, but if it has Biopace, it is probably a Shimano with one of their vintage standard BCDs - 110mm for mountain cranks or 130 for road. Lots of round rings available in those sizes. 110 has since become the "standard" for "compact" road setups, which gives new life to the older Shimano MTB cranks.
3) Mixing tires with slight size differences like that is no big deal. When people do it, they almost instinctively put the smaller tire on the rear, like on muscle cars. Many bike gurus, however, recommend putting the larger one on the front. What you're running is an insignificant difference, anyway. Some manufacturers "25" is larger than some others "28."
4) I have a couple of roadie buddies who would tell you without hesitation that 42x28 is already way into wimp territory. They would rather go through rounds of knee surgery than have anyone spot a 23 cog in their rear clusters.