It's an interesting idea, but I have a few questions:
"We replace the welfare system we currently have, almost entirely, with a regular wage for each person at poverty level. We pay for it all with the money saved from the current system of welfare, combined with an aggressive tax on the rich (some also propose a rollback of military spending)."
A1) How does one define "poverty level"? Are we talking absolute poverty, or relative poverty?
A2) If Google is to be believed, then the UK defines poverty as anyone earning less than 60% of the median income of the average citizen. So does that mean that people who are in part-time work and earning below that 60% will get all of the basic income, or will they get the basic income minus what they already earn?
Suppose the person in part-time work only wants to work part-time (ie; they simply don't want more hours and have made their choice in that matter). Do they deserve the basic income supplied by the government considering that it's their decision to not take on more hours?
B) With regard to the whole "mothers should get paid" stuff, would the basic income be a set amount regardless of how many children they have (effectively doing away with child benefits/child tax credits), or would they get the basic income plus a % based on how many kids they have? If it's the latter, then the playing field will barely go through a noticeable difference seeing as you've got people now having kids so they can get "free money" and a council house. Giving them money via the basic income route wouldn't change that mentality.
I also can't see many people taking kindly to an aggressive tax on the rich simply so that people whose only hobby consists of reproduction have enough money to spend on luxuries (unless the basic income makes the welfare system irrelevant, thus ensuring that the money raised via the taxes can only be spent on necessities and not a second 50" tv).
C) Something doesn't feel right about rewarding people's decision to get pregnant. On one hand, I do think it's kinda unfair that stay-at-home parents don't get financially rewarded for their sacrifices. On the other hand, getting pregnant is still a choice. It's like the whole tax cuts thing with regard to being married; why should someone's personal choices grant them access to money that other people aren't?