Sometimes, but it doesn't have to. It is possible to have the solo completely contrasting from the melody the singer laid down, and make the change rather quickly. Example. Take the chord progression you have up their and have the singer sing to one particular melody. Now the measure before the solo enters, punctuate on a weak beat (say it's in 9/8, stop on 7). On 9 come back in with the same harmony, but kick in a solo in a different tonality as discussed before. Even speed it up a bit. Then have the bass and drums do a 2 bar bridge solo back to the part where the singer goes back to doing his/her thing (chorus line is the most powerful).

Yes it is coherently normal to have the melody that the singer lays down lend hints to what the solo is going to be like, or just have the solo work around the melody the singer uses. The gradual approach as you explained is very effective, but so is a complete change in a split second.

There are no laws governing how the solo should sound in a song. Although following a few to keep a context is exceptionally adequate. An important rule with melody is it has to have a singing tune. But a singing tune from one part of the song (chorus), doesn't have to be the same or anything close to another part of the song (solo). Other factors can tie it together such as harmony, or rhyhtm. The problem is always how to go from one melodic theme to another convincingly.

Another way to hint at a change of major to minor is the supply it will some motives in a relative minor. If the harmony is running in C major, add small A blues minor licks in there. Especially when A is one of the chord tones. Even though the b3 of major and b5 of minor are the same notes. I'm sure you know the b3 resolves to 3 and pulls back to C, while the b5 resolves to 5 and pulls back to A.