I believe your car relies on a vacuum pump to provide additional brake assistance when the engine is cold (warming up). It may be there is a problem with this system, but, please look here: http://repairpal.com/volvo-within-10-miles-of-19060 it's best to have a shop do a thorough inspection of the brake system to be sure the exact issue if found and corrected. To find a shop in your area
This can has a network that connects all the computers in your car. It sounds like there was an issue with the SRS module, or the network. It should be looked at by someone familiar with Volvos. For starters, I would recommend a diagnostic check of the entire computer network, and a software upgrade on the vehicle.
You need to have this looked at, you cannot simply guess or expect someone to guess for you. There are a lot of reasons why it might not be working (bad wiring, switch, sensor, control module etc.), and it's best to have it diagnosed, it will be a better use of your cash.
The solenoid is part of the starter, I'm not sure you can replace it separately. You will need to remove the entire starter either way.
This switch is very easy to replace, takes 2 minutes. But, there was a recall on these switched, so it may be free! http://repairpal.com/volvo-v70-recall-04v504000 Call your local Volvo Dealer, Smythe? http://repairpal.com/smythe-volvo You may get it for free! Good Luck!
Start by having a shop check that the software is all up to date. I suggest going to a Volvo dealer and upgrading all the software in the car, they often have a fix for this and many other driveability issues.
You are taking an approach to fixing this problem that is all backwards. You need to perform a diagnosis first, then replace parts. Start with reading the codes, then troubleshoot accordingly. BTW, you can check your codes for free, without a scan tool. http://www.troublecodes.net/Volvo/ Post the code here and maybe we can help.
You can get repair manuals online for most vehicles, I would try that. I've done this before but I don't trust my memory to provide a step by step.
What is the oil pressure?
You don't need to remove the dash to replace the relay. If you need to remove the dash, absolutely get a repair manual first. Try one of hese online: http://bit.ly/mitchell_repair_manuals_online http://bit.ly/AllData_Repair_Manuals_Online