1. Rather than 'abstract nouns' per se, what we are actually dealing with here is the use of the gerund (a kind - but only one kind - of abstract noun).
2. Although formally identical, gerunds fall functionally into two types: simple gerunds, which combine verbal and nominal (noun-like) powers, and participial nouns, which are simply nouns in -ing derived from verbs.
The difference between them is that the former can simultaneously stand as the subject or object of a verb (like any noun) and yet govern an object and take adverbial modification (like any verb), as illustrated by 'playing' in
 Do you mind my quietly playing the piano while you read?
which both stands as object of the verb 'mind' and governs in turn NP 'the piano' as its own object, whilst being modified by adverb 'quietly'.
Simple gerunds can be determined by possessive adjectives (my, his, etc.) or possessive-case nouns (John's, the doctor's, etc.)** serving to denote the agent of the action, but not by articles.
Thus we cannot have e.g.
[1a] *Do you mind the quietly playing the piano while you read?
A participial noun, on the other hand, is the exact opposite: it can neither govern an object nor take adverbial modification, and it can be (in fact, almost always is) determined by the definite article. E.g.
 The playing of pianos late at night is strictly prohibited here.
where 'playing' connects to its notional object, like any noun denoting a transitive action, by means of a genitive phrase (of pianos), and any modification of it would be by means of an adjective, e.g.
The noisy playing of pianos...
and not an adverb,
*The noisily playing of pianos...
3. Regarding the question of tense-usage, no special conditions or restrictions apply to gerunds of either kind. Thus, provided e.g. a present perfect is deemed acceptable in a sentence according to all of the normal criteria (time frame, etc.), it makes no difference whether the subject of the sentence is a gerund or any other noun or noun-like item.
4. Regarding the appropriate choice between simple gerund construction and participial noun construction, it will be made essentially on the basis of the existence or otherwise of a specific subject. Where an action is conceived of as being performed by a particular individual, we will naturally employ a simple gerund (as in ) , since only then can a subject be specified. When, however, as in , it is understood as applying generally to everyone, then a participial noun construction is the norm.
** N.B. Colloquially, however, objective-case pronouns and common-case nouns tend to serve here, giving e.g.
Do you mind me/Peter playing the piano?
instead of ...my/Peter's...