Bobik shared some more details in private conversation today. I will update the 1st post when I have more free time.
Currently - the cost of war that was mentioned earlier has nothing to do with war declaration (that will still be free) - it's cost to wage war. Building those challenge monuments to fight instanced battles won't be free. And that's what real wars are all about.
For the instanced battles he confirmed again that they are still going with the primetime window. Currently for example 19:00 - 22:00 server time (regional servers after all).
So if the challenge monument is placed on monday 19:30 then the battle will start on tuesday (next day) 19:30.
If you do it earlier like 11:00 on Monday it will start 19:00 on tuesday (earliest timeframe).
If you do it later like 23:50 it will be for tuesday 22:00 (latest timeframe).
And if you declare it on tuesday already like very early at 0:30 then the battle goes for wednesday already 19:00 (earliest setting).
The amount of possible battles depends on the monument level. The currently standart tier 3 monument means you can attack up to 3 guilds in the same evening. Also up to 3 othe guilds can attack you. That means up to 6 instanced battles per evening. For tier 2 it's 2(so 4) and for tier 4 - 4(so8). Tier 1 can't challenge other guilds to instanced battles and can't be challanged by others also. But don't worry - that's not "noob protection". Having level 1 monument means the enemy can go with a siege right away without the chance to avoid such event by winning in the instanced battle.
Each lost battle will burn through the support points and reducing the claim size/monument level. Yes monument can be upgraided back, but it's not instant process (of getting enough influence to upgrade to the next level) and it will be balanced in a way where losing most of your instanced battles won't allow you to avoid the siege event by simply upgrading the monument all the time.
Hope I didn't miss much