Three questions/remarks :

1) "the simple present and preterite can both be used either perfectively or imperfectively." So "He eats a cake" can only have here a imperfective aspect?

2) Just by curiosity: Serbian school grammars, or traditional grammar manuals, state that Serbian has a telicity aspect or that Serbian has a perfectivity aspect?

3) That there can be such a disagreement about the aspect that one language has seems quite stunning. How would you explain that situation? Would it stem from the fact that perfectivity and telicity are not well-defined, or too loose to allow consistent analysis across specialist?

"or in Serbian "Ja sam jela" presents the situation of eating as a single whole, so it is perfective. The situation is also atelic" If "Perfective/imperfective opposition is not grammaticalized/lexicalized in Serbian", and the verb is atelic, how do you tell the verb is perfective here?

To give you satisfactory answers to your questions, I would have to delve deep into the verb aspect cross-linguistically, which is hardly possible in this form. Anyway, "Ja sam jela" can receive perfective or imperfective interpretation, without the context it is anyone's guess which one is in order. This verb form, erroneously understood as "imperfective", doesn't provide the information about the perfectivity of the situation.

"I played football yesterday" refers to an atelic situation seen from a perfective viewpoint. Serbian "Igrao sam fudbal juče" can be either perfective or imperfective, we don't know that, simply because the verb doesn't give that kind of information.

Understood, thank you for your explanation. One thing is still a little bit ambiguous to me "What is lexicalized is the telicity of the verb - each verb is clearly telic or atelic"

Telicity in serbian is a grammatical aspect: it is marked with with inflection; or is it a lexical aspect: it is inside the meaning of the verb, without any specific grammatical indicator?

And here "Ja sam jela", is the form inflected in any way which would mark (a)telicity?

The key characteristic of Slavic languages is that they are morphologically very complex. The (a)telicity of the verb is partly inferable from the set of morphemes that "tweak" the stems of verbs, creating the telic/atelic counterparts to the base verb. Very roughly speaking, prefixes are telicizers and suffixes are atelicizers.

The interaction of morphemes and verb meanings is very intricate so mastering the verb aspect can be a daunting task to those bent on learning a Slavic language. The semantics of the verb together with the set of morphemes define its telicity. To put it simply, the base form of the verb can be either telic or atelic (depends on the verb's semantics) and it is either prefixed or suffixed to get the telically opposite counterpart.

Telicity, inchoativity, durativity etc are semantic aspects of the verb that may or may not have grammatical expression in language. Serbian doesn't have separate grammatical forms for progressive/habitual/imperfective or perfective aspects. English has a dedicated progressive form, and its perfective counterpart, and it has would and used to as markers of habitual aspect.

It would be more proper to say that telicity, inchoativity etc are "properties" of the verb, rather than "aspects" of the verb, not to confuse these concepts with the lexical and viewpoint verb aspects. "Jesti" is an atelic verb whose telic counterpart is "pojesti", with (obviously) the morpheme "po" turning the atelic stem into the form that expresses the completion of the eating event.