The gender may be surplus to requirements when determining the correct form of byc
Luckilly, for the present tense this requirement doesn't exist for the word być. Just in case you're still struggling a little, let's start with some basics. I will make some statements that might seem to those in the know as not really rules, but for now I may be rounding some things up.
The simplest sentence in Polish requires two parts:
Subject + Predicate i.e. (the person or object who/which performs an action or activity) + (the activity)
Actions can be performed by an individual subject, or by a collection of subjects. For instance "I am" or "we are". The bolded words are subjects, the ones in italics are the activities. Here the bolded words happen to be also so called personal pronouns, i.e. words generically denoting a person. When I speak about actions I perform, I will use the personal pronoun "I", isntead of my fist name.
When I say "John is whatever" then I am not using a personal pronoun, but if I continue talking about Jonh, I don't need to continue using his name. Instead I will use the personal pronoun "he". I hope this is logical to you. In short, personal pronouns specify (in Polish and in English, among others) the number of persons performing an action (one or more i.e. singular or plural), and sometimes the gender. What is also important, the persona pronoun describes the relation of the speaker to the person who performs some action.
Speaking about myself I will say "I am doing something". I am one person so the personal pronoun is called 1st person singular. Yup, grammar acknowledges the egotistic tendencies in humans. The enumeration of personal pronouns always starts with I. It's a rule.
When I speak to one person directly I will address them by "you" (second person, singular), but when I talk to anybody about actions of a person not being addressed, I will use she, she or it - this will be 3rd person singular.
The good news is: this is the end of personal pronouns, but , the bad news is: thus far we dealt only with singular form of personal pronouns. Let's recap before hitting on the plurals
English - Polish
1st person singular: I - ja
2nd person singular: you - ty
3rd person singular: he/she/it - on, ona, ono
The above is to be remembered for ever and ever. Amen.
Plural forms are pretty much direct derivatives of of singular forms, and the order in which we enumerate them starts from within and goes outward too, i.e. again in the egocentric fashion. The plural form for "I" is "we", you doesn't change in English but it changes in Polish. Let's look at the table below:
English - Polish
1st person plural: we - my
2nd person plural: you - wy
3rd person plural: they - oni, one
Another table to remember till your last breath, or at least as long as you speak a foreign language
In the above you will notice some differences in the number of pronouns for both languages for 3rd person. "They" is a collection of persons or object. In English "they" will be used regardless of the gender of individual components of that collection, but not so in Polish. The rule is simple: if at least one member of the collection (3rd person, plural) is male then "oni" is used. Otherwise "one" is correct.
Just a side note, and to be sure you understand; in the plural forms table, when we call a pronoun 1st or 2nd or 3rd person, the word person is a grammatical concept, so it the word itself does not assume plural form.
Let's put the personal pronouns and "być" together in another table:
English - Polish
1st person singular: I am - ja jestem
2nd person singular: you are - ty jesteś
3rd person singular: he/she/it is - on/ona/ono jest
1st person plural: we are- my jesteśmy
2nd person plural: you are - wy jesteście
3rd person plural: they are - oni, one są
Notice that within the same person of the same plurality the form of the word "być" does not change. So "ona jest" and "on jest". This is exactly the same as in English.
In your original post you appear to be unsure what forms of "być" to use when the subject of the sentence is a name. This requires a quick mental substitution and things become clear.
Using some of your examples:
There is one Michel. Nobody accompanies him in the sentence, so we know it's singular. Half of the job is done.
You are not Michel, so the form of "byc" for 1st person singular (I) does NOT apply.
You are talking to Michel so form for 2nd person singular (you) does NOT apply.
The only one left is 3rd person singular, i.e Michel = he. If that was Michelle then the personal pronoun to use as a substitute would be "she".
Thus we arrive at the final answer Michel is 3rd person singular, so the form "jest" will apply.
Similar process will be used to take care of the other examples.
Agnieszka i Robert - more than one person, so they are plural
They are not you, and they are not who you are addressing. Instead they are who you are talking about, so they are 3rd person plural.
OK< I hope I didn't make it harder than I thought it was for you before this post.