Answers to your questions:

1. The arrival of the Jews chased out of germany in the mid- 14th century by the "Black Death" and mass killings, into the expanding feudal Grand Duchy of Lithuania (GDL). With the privileges (rights) granted them by the Grand Dukes, Gediminas (1316-1430) and Vytautas Magnus (1380-1430), and later on, under the direction of the state ackowledged Jewish Va'ad (Counsil) (1623-1764), they carried on an autonomous community life in the Grand Duchy for a period of 400 years. The Jews contributed a great deal to the GDL, and in the time its capital city of Vilnius became a Jewish spiritual and religious center. Before 1800 A.D. the population of the GDL included 250,000 Jews.

The earliest Jews received Southern West part of Lithuania.

Nows it's a little bit difficult for me to answer when exactly Jews become part of Rumsiskes. I will try to clear it as quick as it would be possiblle in archive. According with V. Sirokomle (Polish poet) "in 1860 Rumsiskes were full of Jews". There were Jewish school in 1831, a synagog in 1861, a public house. There were more than 100 Jewish families before First World war. It is believable that Jews in Rumsiskes in the middle of 17th century.

2. The Jews in Rumsiskes were merchants, traders, artisans/any of them were occupated in floating of wood by river to Russia.

I found in "Jewish encyclopaedia"(Vol. 9.Sankt-Peterburg.1907-1913, in Russian) few days ago that there were 308 Jews in Rumsiskes in 1847, in 1897 there were 411 Jews (1.180 inhabitants at all).

I found some material about the Jews in Rumsiskes (since 1833 until II World War) in hebrew by Dov Levin "Pinkas Hakehillot" (Jerusalem,1996).

Few interesting sentences about people of Rumsiskes from article "Old Rumsiskes" by A. Miskinis in book "Kauno marios". Vilnius. 1981.
Pages 59 - 60: In a document of 1798 there is mentioned that merchants of Rumsiskes (two of them were very rich) were occupied in iron, wood, salt, trade. Salt was brought from Karaliaucius (Kenigsberg). Wood was sold in Vilnius or in Prusia. There lived 38 Jews in 13 houses.
Page 61: 30 pupil attended school of Rumsiskes (5 of them were Jewish) in 1830.
Page 612: There were 85 Jews families in Rumsiskes 1852.

About 700 Rumsiskes Jews were killed on August 29, 1941 in Pieveliu village (now territory of Ethnographical museum). I don't know how exactly they were killed but it is possible to look for the information in archives.