> (1) So it’s okay for me to sell the eggs from the chickens on my property, as it’s not using others’ labor?
Probably (the “on your property” bit is pretty irrelevant here, the chickens are the relevant property.)
> (2) Now if everybody likes the eggs, and I start paying a neighbor to help out with the chickens because it’s too much work for me alone, would the government then take my land / take me away?
Details of policy can vary considerably within the Marxist theoretical framework (and finding concrete examples is impossible as there aren’t any places that have really applied anything in this area of Marxist property approaches without Leninist modifications); fairly typically, in theory, the government would require the enterprise employing labor outside of the individual worker/owner (or possibly family) to be either public or collective, and contracting for labor on other terms would either be void or, I guess, might presumptively create a collective notwithstanding the surface terms. The penalty, if any, for a prohibit wage-labor contract (besides the contract itself being void) isn’t really a matter of general Marxist theory but of the praxis of the particular society in its context.
> (2) Now if everybody likes the eggs, and I start paying a neighbor to help out with the chickens because it’s too much work for me alone, would the government then take my land / take me away?
Classical Marxist theory, being conceived in the 19th Century, didn’t really concern itself with large-scale, labor-free automation, but given Marx & Engels views on taxation – favoring direct, progressive, and significant taxes on income (capital and otherwise) and inheritances, as well as significant land-value taxes, etc. — it is certainly not outlandish to suggest that one Marxist position would be that you would be permitted to operate such an individual enterprise, but that as your returns from it increased in scale that they would be progressively more heavily taxed. You could, though, accumulate wealth that way, but not without constraints.
Of course, some of those limits are present in many modern mixed economies (even with the allowance for rented labor), as tax ideas advocated by Marx, Engels, and others in the same Communist movement — very much in contrast to their ideas on property — were among their ideas that saw the widest success in the developed world in the transition from the classical capitalism that Marx critiqued to the modern mixed economy that generally replaced it.