Eviction Rights

Every lease can be different, but in general the new owners would have to respect the terms of the lease.

Unless they planned on selling during your sisters tenancy, its unlikely that there is wording to the contrary...

There are two typical types of forms of condo rental contracts out there - one by the Real Estate Board of NY and one by Blumberg. I don't have the REBNY version, but I do have a copy of the Blumberg. Section 17 of the Blumberg lease form states: 17. Sale of Unit: If the Landlord wants to sell the Unit, Landlord shall have the right to end this Lease by giving 30 days notice to Tenant. If Landlord gives Tenant that notice then the Lease will end and Tenant must leave the Unit at the end of the 30 day period notice.

So to continue, the Landlord merely needs to take steps to sell the apartment for this clause to go into effect. Unless there is another clause in the lease that would supercede, such as a right of the tenant to renew, which is often a provision added (i.e. non standard) for other reasons to the lease.

Furthermore, to continue, there are always three things going on:
1) Contract - specifics addressed above. This will prevail in an eviction in court, unless statute or precedent takes over (e.g. the pet rules ... the contract may say no pets, but if you had a pet for X period of time and no one had a problem with it, the law would allow you to keep it.)
2) Relationship. Lots can depend on the relationship between the two. Often just a conversation and good relationships will prevail. Of course, not always. But its always the first thing to explore.
3) Lawyers. Lawyers aren't right or wrong. They just fight. But often having the most intimidating or aggressive attorney can win a point prior to court, but after the relationship has failed. They could also be expensive.

Lastly, with respect to the open houses, your sister's accommodation should be reflective of how she is acting in the relationship, which she should use to support her case in a conversation with the landlord. The landlord has the right to end the lease within 30 days, and has the right at reasonable hours (typically thought of as business hours during the week, but there is no rule) to show the apartment to a prospective tenant or buyer. But outside of reasonable hours, and with high frequency, probably not (again, see the discussion of contract, relationship, and lawyers). Also, the landlord is allowed to show it, and the tenant could argue that the landlord, not the landlord's surrogate, must be present for the showing. But ultimately, the ultimate provision is the 30 day termination, which the landlord could seek to exercise if the tenant is otherwise uncooperative.

Best suggestion - have a conversation. Seek an understanding of a minimum time for eviction (put it in writing or an email) and when open houses can take place. Ask for a rent reduction if it is sensible to do so, especially if by having open houses she needs to keep her place clean, organized, etc.