How to express that someone is old? If I am talking about someone, and want to indicate that they are very old (not in a negative way, just stating a fact), how do I do that? 

Something like this?
他是老人
'他是個老人' - 'he is an old man'

It is a plain statement. The classifier 個 should not be omitted because 老人 could be a noun or adjective. '他是老人' sounds like your sentence is incomplete. Using the classifier 個 indicates it is a noun and it is a complete sentence (not &quot;他是老人... 恊會的主席&quot; )

'他是個老人家' - 'he is an elderly'
'老人家' is more respectful term than just '老人'

Notice '他老人家' - (he the elder) is a respectful way to address someone senior in age, or high in status.)

'他是一名長者'- 'he is an elderly'

The classifier for '長者' (senior/ elderly) should be those that reserved for human only, like '一位' or '一名'.

'他是個上了年紀的人' - 'he is a man of advanced age'

A matter of fact statement