What are the effects of adding water after the boil?

If you have designed your recipe to account for adding the extra water at the end of the boil, then I see no issues what so ever.

I would personally add a couple of litres of boiling water every 10 min or so rather than adding it all at the end, just to avoid over concentrating the sugars in the wort, which may encourage caramelisation & Maillard reactions and hamper hop utilisation. However, it depends what you want from the brew, these may be desirable in your brew.

I add nearly freezing water to chill it quicker to pitch temperature. 1 gallon of near frozen I add to 4 gallons of wort to chill it to lager pitch temperature quicker. Once my immersion chiller cannot reduce the temperature any further, I introduce the near freezing water into my wort. I do not notice any negative effects. The hops are still very nice tasting.

There are two potential, but not serious, issues with boiling the volume lower than full: 1. Maillard reactions (not caramelisation) at higher wort gravity tend to be more prominent. Sometimes it's good (e.g. when you boil down first runnings when making dubbel), other times not so good (witbier and other light stuff). 2. Hops tend to be under-utilised in smaller volume boil. This is a common-sense based wisdom, but kinda difficult to measure.

For these reasons boiling the full volume is more predictable.

I like to streamline my brewing processes as much as possible, hence find preparing extra sterile water for diluting wort an extra trouble (btw you don't need sterile water for mashing, just tap water - corrected for chemistry - is good enough). If I were you, it would be getting a bigger kettle (in fact, I have 50l one).