1) In terms of the prohibition of a non-Jew performing prohibited activity for a Jew on Shabbat (''Amira Le'Akum''), there is nothing wrong with renting out one's property to a non-Jew, because all the profits are going to the non-Jew and therefore he is working for himself, not for the Jew. The reason that the Sages prohibited renting one's premises to a non-Jew in certain cases, like a bathhouse, is due to the prohibition of ''Marit Ayin'' (lit: visual appearance), which forbids the performance of a permissible act, if a theoretical witness (who knows Jewish law) might mistake it for a forbidden one. Fields and mills were usually either rented fully to the non-Jew (where the non-Jew receives all the profits) or the non-Jew was hired and worked for a share in the profits. Therefore, those who saw a non-Jew working on Shabbat in a Jewish-owned field or mill, would have no reason to suspect that the Jew has violated the prohibition of employing a non-Jew on Shabbat by hiring him as a laborer who doesn't receive any share in the profits. Bathhouses, on the other hand, were not usually rented out fully, nor were workers usually paid with a share in the profits; therefore, the Sages prohibited renting out a bathhouse to a non-Jew, because those who see a non-Jew working on Shabbat in a Jewish-owned bathhouse, would likely assume that he is a hired worker who doesn't receive a share in the profits, and that the Jew has violated a prohibition by allowing a non-Jew to work for him on Shabbat.} 2) If the Jew is only renting the premises, the property would not be regarded by the public as Jewish-owned (i.e the Jew's name would not be associated with the property), and therefore a non-Jew working there on Shabbat, would not be viewed as an employee of a Jew (See Rema 243:2 and Mishna Berurah). 3) Some texts add different kinds of guest houses/hotels to the list. 4) This prohibition of renting one's business premises to a non-Jew who will be working there on Shabbat, is entirely dependent on local custom. If the local custom is to hire out the particular premises under a rental agreement, there is no prohibition.

1) The reason for not allowing a non-Jew to perform Melacha in a Jewish home on Shabbat, is based on the principle of ''Marit Ayin'' (lit: visual appearance), which forbids the performance of a permissible act, if a theoretical witness (who knows Jewish law) might mistake it for a forbidden one. In this case, people might think either that the Jew, on Shabbat, instructed the non-Jew to perform the work for him, or that the Jew has hired the non-Jew for the day, both of which are prohibited. Even in cases where ''Marit Ayin'' would not apply (e.g. where the non-Jew is obviously a contractor, not ''hired for the day'', and it is clear that the Jew didn't give the instructions on Shabbat itself), there is still the issue of "Zilzul Shabbat" (Contempt of Shabbat), whereby the sense of the holiness of the day might be reduced, if certain activities are being performed by a non-Jew in a Jewish house (See Igrot Moshe O.H 3:35). Any Melacha that attracts attention because of its noise, like a vacuum cleaner, constitutes "Zilzul Shabbat." (See Rema 252:5) 2) One of the 39 types of forbidden activities on Shabbat. 3) Other authorities permit it under certain circumstances (See Mishna Berurah O.H 244:30, and next footnote). 4) There are those who permit it if the servant is obviously doing the Melacha for his own benefit and none of the other problems apply. (See Mishna Berurah 244:30)

בביתו של ישראל אסור להניח לאינו יהודי שיעשה מלאכה בשום אופן ואפילו משרת אינו יהודי שרוצה לעשות מלאכה בשביל עצמו צריכין למחות בו

1) If only the finishing touches were made on Shabbat, but it was wearable already on Friday, one is permitted to wear it on Shabbat (Mishna Berurah 252:30). 2) On the Shabbat, rather one must wait the amount of time after Shabbat that is equivalent to the time the non-Jew spent working on it on Shabbat. If the goods were needed for a mitzvah, one may use them immediately after Shabbat. 3) Other authorities (Shulchan Aruch 252:4) rule that it is permitted to wear the garment on Shabbat, because the non-Jew was working on Shabbat for his own sake, that is, to finish the job faster, and get paid. Nowadays, we follow the more stringent view. 4) This is permitted because no one would suspect that this non-craftsman was instructed to make shoes on Shabbat for the Jew. The Rema (252:4) permits it even if one was taking from non-Jewish craftsmen, as long as this craftsman would make shoes in bulk to sell to the public, and no one would suspect that he had made the pair specifically for the Jew on Shabbat. 5) If one did mention the price, one will have violated the prohibition of buying and selling on Shabbat, even though no money was transferred as of yet. 6) Shabbat boundary - see Chapter 95.