Me. Myself is reflexive: it denotes that the person (me) is doing something to that person (myself) and no other. It's not correct to use a reflexive pronoun unless the recipient of the action is the person doing that action. You can't mix you with myself. You can talk to me. I can talk to myself.
Saying free or available rather than busy may be considered a more "positive" enquiry. It may also simply mean that you expect the person to be busy rather than free, rather than the other way round. Saying available rather than free is considered slightly more formal, though I wouldn't worry much about usage cases.
"Free" is an adjective, applied to the noun "will". In keeping with normal rules, a hyphen is added if "free-will" is used as an adjective phrase vs a noun phrase.
The fact that it was well-established long before OP's 1930s movies is attested by this sentence in the Transactions of the Annual Meeting from the South Carolina Bar Association, 1886 And to-day, “free white and twenty-one,” that slang phrase, is no longer broad enough to include the voters in this country.
My company gives out free promotional items with the company name on it. Is this stuff called company swag or schwag? It seems that both come up as common usages—Google searching indicates that the
3 There is no universal one-word replacement for -free. In the context of foods the appropriate portmanteau is gluten-containing -containing can be used universally, although there are other alternatives depending on specific food components (eg, sugared for sugar-free)
By contrast, its father (who might have been thought responsible by some) could be adjudged blame-free when another explanation is found. On the other hand, the mobile telephone that can be used in a hands-free manner would not sell very well if advertised as being hands-less.
The most obvious more formal way to say 'I'll free up time…' is simply 'I'll make time…' but neither is in any way appropriate here. You need 'I'll do it by/on Tuesday' or 'I'll do it right away' and in either case, you need to stick to it.
With the advent of the free software movement, license schemes were created to give developers more freedom in terms of code sharing, commonly called open source or free and open source software.