Do I need my own piano or guitar to start?

You will certainly need to have access to an instrument, but it is not advisable to rush out and buy one without plenty of serious thought and research.

Piano: initially some sort of electronic keyboard should do well enough to get you started, and as with guitars, you will probably find that a friend or acquaintance has one that they’ll be happy to lend.  Later you will need either a ‘real’ piano or a digital one.
The worst thing to do is buy an old piano in poor condition; it may be cheap, but will soon become a white elephant: toneless, worthless and difficult to dispose of.

Guitar: you might try to borrow one from a friend or acquaintance; music shops often recommend large, heavily-strung guitars to beginners, and this is rarely a wise choice.  Buying second-hand is risky, unless you know exactly what to look out for; guitars (especially inexpensive ones) generally deteriorate over time.

How much will I need to practise?

The secret is to practise every day, even if it is only for 10 or 15 minutes at first. Once you have longer pieces and studies to prepare, your practice time should be extended accordingly.

Am I too old or too young to learn?

The short answer is ‘no’; once a child can read simple texts etc. he or she is ready to begin learning a musical instrument. The elderly: provided they are keen, and willing to practise diligently, they will make progress, and should find it very involving and satisfying.