the OP is actually doing a border bounce, not a visa run. And to answer your question, yes, you must attend the Laos consulate in person to pay for your visa.
If applying in most Western world nations there is no or little seasoning requirements. You must somehow demonstrate financial stability. Don't know why you talk about a deposit certificate when what they want to see is the money in your bank or see your parents bank statement along with the sponsorship letter.
TM28 is notification of change of address. Typically a TM47, 90 day report notification is stapled in, sometimes a TM28 but it's not really been used in the last few years