A few questions regarding info for employers (careers and employment)?

Q1) say I apply for a job that advertises a £20,000 - £23,000 salary. I have very little work experience (though qualifications are good) and would be willing to work for less, say £17,000. Should I write in the cover letter that I'd be willing to work for less than advertised? If so, should I write an amount (exact, or approximate?).

R1) Absolutely not do not put a salary where either you want the highest level they or paying or lower than offered, under any circumstances, in a cover letter or resume.

Q2). I finished college in July. I took the summer off and started applying for jobs in September. I haven't had much luck (1 interview) but have been demotivated and haven't been looking as much recently. If an employer asks why I've been out of work since july, what should I say?

R2) There is only a three (3) month lapse in time since you graduated college, which is not unreasonable, there are millions of experienced education people who have been out of work for a year or more. If asked the question just simply state you took some time off after being 2 or 4 years in college and you are now ready to pursue work/career. Good Luck.

Credentials: Work Force Instructor for the unemployed (5 years) i.e. resume writing, interviewing, job search etc. Vice President in a Bank for 30 years managing 20 people/interviewing/hiring/firing

Question number 1

Put down that you want £20,000 or £21,000. Don't sell yourself short.

Question number 2

If you finished college in July I think you are fine - I doubt if the question will even come up but if it does you can just say you have been looking for positions since your graduation. No one is going to ask you how many applications you sent out each week, etc.