*"Doing the work he was sure." [incorrect]

This is a not a complete sentence (even though "He was sure" by itself is). In answer to your question, yes, you are correct that adding a comma would make it OK, but we would still be left with questions ourselves, such as "What work?" and "He was sure of what?" Let's "change it up" to make this work:

While doing the math himself, he realized his teacher had made a mistake. [correct]

Let's look at the other example:

"Meeting you, I was proud." [correct but perhaps confusing]

It's OK as it is, but it leaves us with more questions again, such as "Why would I be 'proud' about meeting you?" or "What is it about 'meeting you' that would make me proud?" It doesn't make much sense in real life. So let's try this instead:

Meeting you, my heart filled with joy because I have long admired you. [correct]

There is no ambiguity here about why "meeting you" would cause you to feel a certain way. I think you have a good grasp of using present participles if these additional examples and explanations make sense to you. The problem was with the original examples, and you were right to question them.

*"Doing the work he was sure." [incorrect]

This is a not a complete sentence (even though "He was sure" by itself is). In answer to your question, yes, you are correct that adding a comma would make it OK, but we would still be left with questions ourselves, such as "What work?" and "He was sure of what?" Let's "change it up" to make this work:

While doing the math himself, he realized his teacher had made a mistake. [correct]

"While" makes it clear that his teacher's error occurred to him while he was busy solving the math problem. If we want to indicate he had completed the math before drawing his conclusion, we could say,

"After doing the math himself, he was sure his teacher had made a mistake." [correct]

Let's look at the other example:

"Meeting you, I was proud." [correct but perhaps confusing]

It's OK as it is, but it leaves us with more questions again, such as "Why would I be 'proud' about meeting you?" or "What is it about 'meeting you' that would make me proud?" It doesn't make much sense in real life. So let's try this instead:

Meeting you, my heart filled with joy because I have long admired you. [correct]

There is no ambiguity here about why "meeting you" would cause you to feel a certain way. I think you have a good grasp of using present participles if these additional examples and explanations make sense to you. The problem was with the original examples, and you were right to question them.

*"Doing the work he was sure." [incorrect]

This is a not a complete sentence (even though "He was sure" by itself is). In answer to your question, yes, you are correct that adding a comma would make it OK, but we would still be left with questions ourselves, such as "What work?" and "He was sure of what?" Let's "change it up" to make this work:

Doing the math himself, he was sure his teacher had made a mistake. [correct]

Let's look at the other example:

"Meeting you, I was proud." [correct but perhaps confusing]

It's OK as it is, but it leaves us with more questions again, such as "Why would I be 'proud' about meeting you?" or "What is it about 'meeting you' that would make me proud?" It doesn't make much sense in real life. So let's try this instead:

Meeting you, my heart filled with joy because I have long admired you. [correct]

There is no ambiguity here about why "meeting you" would cause you to feel a certain way. I think you have a good grasp of using present participles if these additional examples and explanations make sense to you. The problem was with the original examples, and you were right to question them.

*"Doing the work he was sure." [incorrect]

This is a not a complete sentence (even though "He was sure" by itself is). In answer to your question, yes, you are correct that adding a comma would make it OK, but we would still be left with questions ourselves, such as "What work?" and "He was sure of what?" Let's "change it up" to make this work:

While doing the math himself, he realized his teacher had made a mistake. [correct]

Let's look at the other example:

"Meeting you, I was proud." [correct but perhaps confusing]

It's OK as it is, but it leaves us with more questions again, such as "Why would I be 'proud' about meeting you?" or "What is it about 'meeting you' that would make me proud?" It doesn't make much sense in real life. So let's try this instead:

Meeting you, my heart filled with joy because I have long admired you. [correct]

There is no ambiguity here about why "meeting you" would cause you to feel a certain way. I think you have a good grasp of using present participles if these additional examples and explanations make sense to you. The problem was with the original examples, and you were right to question them.