Migration:

1. An UBI would only be given to state citizens obviously.
2. Also when every state has UBI (which is actually cheaper for poor countries and way more effective there), the migration will surely be lower then under the current wars, economical destruction by the West and climatic destruction caused by the west.

Jobs: You make the basic wrong assumption that under UBI nobody would work for money. But that is not true. Most would still do it. The only thing that will change are the amounts you get for some jobs. Maybe cleaning will be a high paid job (so most people decide to do it themselves).

And why do you think

with tasks relating to law&order. Do you really want to filter out all those who the jobs without being particularly fond of it

?? It will acutally be the the other way round, people are way more likely to do what they want, and there are a lot of people who want to do police or doctor not because of money but because they want to help.
Also dont forget that a huge part of crime has its roots in poverty. UBI will decrease that dramatically.