Need help with wordpress site from Spam attacks

My host admin keeps disabling one of my accounts on the server and i am told that it is getting attacked and bombarded, i have askismit running and math problems on comments and login. Now apparently there is updated for everything to fix security flaws the site is a little old but i keep running into errors whenever i update. Same as others i have had to limit upgrades on a few custom builds from errors.

Is there certain things to change to be able to take a core and theme update?

How is the website being attacked? For example is it a DDOS attack? Or are you just receiving tons of spam in your comments areas?

What sort of errors are you getting when you update?

i will move the site to offline server and do it on a home server and shall update with exact things. Also there has been some DDOS latly so i am getting blamed for it. lol