NOT A TEACHER.
I've just got my pre-interview task and am feeling quite daunted by it. Mine focuses on verb phrases.
Though to get back to you. I would answer it something like this:
1) The difference in meaning is that a) implies everyone at the party was waiting for you, perhaps it was a party thrown for you or even that it was a boring party until you got there and liven things up. Where as b) implies that the party had begun before you arrived.
To help students understand the difference I would perhaps suggest a little role play. For a) maybe have a group of students 'pretend' to throw a surprise party for another student. Have them walk through the door, then the 'party' begins. For b) perhaps have a student pretent to arrive late to a party.
2) The difference in meaning is slight. While both a) and b) suggest someone or something has got involved with an activity or event to change the outcome, a) could be beneficial or negative whereas b) generally has negative implications on the outcome of the event. For example if someone is dying, a doctor may intervene to save their life. You wouldn't say the doctor interfered. Interfere generally has a 'stopping' effect and negative implications.
To help students understand this I would again suggest role play of different scenarios and ask students to suggest which word they would use.
E.G. - The doctor......to save the mans life.
'Do not........with my work!' Yelled the angry businessman.
If it was not for the police who..........the robbers would have escaped.
Hope this helps.
Like I said, I am not a teacher and have not passed a CELTA course, and am doubtful I will anytime soon. I'm just a native who likes helping out on this forum when I can.