Yes, it's called sufficient pay. Removing the wage mechanism only has the impact of poor allocative efficiency and puts resources and capital into the less productive activities.
I doubt that you could pay people enough to do these jobs. The Roman Empire often functioned at the end of its technological tether, and things like mining and quarrying were horribly unsafe. Of course a society could adapt - you would have, say, less ashlar and more brick, some mines closed down, more privately allocated mining "shares" etc. The problem is that Rome would have had to consciously choose that path and thereby forgo measuring up to the glory of its predecessors (who had used slave labour in mines and quarries).
I disagree. Trade, agriculture and resource supply all get done in non-slave economies. All that would happen would be a movement from the latter two to the former. What it would mean is that a larger consumer class would develop, and less people would be living in the lap of luxury without needing to work themselves. Both are good things for economic development.
Well, agriculture tends to get done because pewople have to eat, and trade is not terribly arduous. But there are many things that, while immensely profitable and glorious, tend to involve dangerous and unpleasant work and not be strictly necessary. You have to force people to do that kind of work. Granted, they don't havbe to be slaves. Indentured servants, Boer "apprentices", indigent factory hands driven off the commons and threatened with deportation and the workhouse, sharecroppers, debt servants, colonial "squatters" or prisoners can all be roped in. But the problem remains that some work will not get done unless people are either forced or bribed to do it, and the Roman Empire can't really afford the bribes.
The problem of a lack of currency is such a large one it inevitably becomes solves very quickly. What would likely happen is that gold becomes much higher value relative to the smaller coins, and a different denomination system simply gets set up. There's always the possibility of other medium of exchange, such as paper money, springing up, as happened in 18th Century America, despite opposition from central government. Needs force innovation.
If it was done, it is likely some solution would be found, but keep in mind that breaking the currency system without newed would be a horrifying idea to the Roman elites. It would also very likely involve painful readjustment, especially painful for those whose wealth is in money. Like wage labourers.
Again, this is something that would develop fairly quickly to address needs. Either you get debt bondage, or people start saving up money to join guilds and get themselves trained up as happened in medieval Europe.
And again you are proposing breaking the system on the assumption that a solution will emerge. It's not that I don't think it would be possible, but what sane politician would agree to actually doing this? we are discussing the idea of a Roman abolition, and I doubt you will convince anyone of its viability through the Rumsfeld school of nation building. Imagine putting this to the senate or the consilium - you'd get laughed out of the session.
I'm really not sure what point you're making here. What do you mean by "wanting to be an empire"? Conquering other peoples? That's happened under plenty of societies with free labour. Non-permanent conscription is always possible along side a free economy, but even so, it's not needed, as the spoils of war are generally payment enough.
I mnewan that a society that aims to be an empire, as in, exert dominion over others for its own gain, needs to be able to command unwilling labour. There are different ways of doing it, but the dominant modes in the Roman world were slavery (for outsiders) and the dilectus (for Romans). You will not be able to abolish coercion and stay an Empire, so what would the motivation for changing its form be?
I think you've got cause and effect the wrong way round. More sophisticated forms of economic arrangements were held back by the presence of slavery. If society has a big changes, new ways of dealing things inevitably come in. Abolition in the Roman Empire would create better allocative efficiency, more innovation, more economic growth, and likely the creation of a larger middle class that would further help.
If it survived the massive dislocation first. Pulling off a coordinated manumission of probably millions, certainly many hundreds of thousands of slaves, transfering them into gainful employment, and doping all of this while keeping their former owners satisfied and continuing to operate the established forms of state largesse and imperial prestige spending (not to mention the military) is a task that I doubt the Roman Empire was up to.