Can someone explain compound, simple, and run-on sentences in a lengthy paragraph if you can? if so, i you dearly for i am reviewing last year's subject, and i'm struggling with it slightly.

jan went on a quiz show, won two hundred dollars, and bought gifts for her family.
my guess for this one would be a compound sentences, but it would also sound correct if i pt the sentence like this--
jan went on a quiz show. she then won two hundred dollars, and bought gifts for her family.
therefore, it could be a run-on sentence.

the museum was crowded, but our group was able to see everything.
my guess is a run-on sentence for this one, but then again in second grade i had learned to never use the word "but" as the starting point in a sentence. so that's where i'm deeply confused.

my puppy is well-trained; he can sit and speak.
i'm fond of semicolons, but they can confuse me at times. this is one of those times. anyway, my guess is a simple sentence, but simple sentences usually don't have any punctuation besides the period at the end.

therefore, am i correct on any of these?

A compound sentence is at least two independent clauses that have related ideas for ex. I like soccer, (1 clause) and he likes basketball. (2 clause)

A simple sentence is only one independent clause for ex. The report is complete. (1 clause)

A run on sentence is two or more clauses. The sentence is crowded no stopping periods just commas. For ex. The corporation is packed with goods and services, and the goods are produced daily, customers love our products, sales and profit rise- more competition.

1. Your correct it is a compound sentence because there is at least two independent clauses and most importantly the ideas are related. "Jan went on a quiz show, (1) won two hundred dollars, (2) and bought gifts for her family."

2. The museum was crowded, but our group was able to see everything.(1) after the comma you count each sentence to see how many clauses. After the comma in this sentence there is only one clause so the answer is simple sentence

3. My puppy is well-trained; he call sit and speak. Semicolons are only used to complete a sentence.
As a matter of fact, as long as the sentence has one clause then the sentence is automatically a simple sentence. Semicolons are used to complete a sentence so they don't produce another clause. That is a simple sentence.

As long as you count the sentence after the comma(s) you can determine if it is a compound sentence- all related information 1, 2 or even 3 clauses, a simple sentence only 1 clause- supporting punctuation (semicolons) doesn't affect the sentence, and run on sentence heavy info in just 1 sentence with many commas.

Hope this sheds some light :)