Credit Score Management

I am wanting to buy a house, but I don’t want to look into financing until I find something I like. I am worried my credit score will be reduced if I start asking banks to review my credit.

I received a letter in the mail from Juniper (iTunes Rewards) stating that they have closed my credit card account due to inactivity. I opened the account about 18 months ago and have never really used it. Can they close my account just like that without any warning? How should I handle the situation? (Is there anything I can even do?)
Also, I know that closing credit card accounts lowers your credit score. Does anyone know how much mine will be affected?

I have 5 negative reportings on my credit report. None of them are after the year 2004. I am wondering since there over 4 years ancient, how much are they affecting my credit score? And, has anyone ever heard of credit card companies deleting accurate late pays if questioned?

I recently went over my credit limit by $10 and noticed that the credit card account (Cap One) was reported as delinquent on my equifax credit report? How can this happen and what are the consequences to my credit rating/score? Thanks for your response.

If someone has a credit score of 750 and gets sent to collections what will their credit score look like? I want a numerical answer and not one of those “it stays on there 7 years” responses. I know that once you pay it off you can dispute it, how do you go about doing that?