Your last question can be answered here:
''Plymouth Brethren, group of Christian believers originating in the early 19th cent. in Ireland and spreading from there to the Continent (especially Switzerland), the British dominions, and the United States. One of their notable leaders was John Nelson Darby; the members are sometimes known as Darbyites. They refer to themselves as Brethren, Christians, or Believers. In a reaction against the formality of prescribed ritual, the requirements of ministerial ordination, and other established conditions in the churches of the times, groups of believers began to meet independently in Dublin and elsewhere for spiritual communion. Associations were formed c.1828 in Dublin and c.1830 at Plymouth, England, whence the popular name Plymouth Brethren. Brethren hold differing opinions concerning baptism and expect the personal premillennial second coming of Christ. The Lord's Supper, as a commemorative act of worship, is observed once a week. Followers of different leaders withdrew from time to time from the main body to form new congregations. This tendency to divide was carried over into the United States and Canada by emigrants, who established new meetings of the Brethren there. In the United States there are eight separate divisions, some of the exclusive type, stressing congregational interdependency, and some of the open type, stressing the independence of congregations. Basically fundamentalist, the Brethren consider the Scriptures the only true guide. No officers are chosen to preside over the congregations; the privileges and duties of the ministry depend upon the personal gift of the individual member.
Regarding the hair & clothes, I have been told that the brethren live by 'very simple' means which advocates plain clothing. I am not sure as to why the hair is covered, but I suppose I would liken it to nuns or muslim women (who often wear traditional dress, whilst the men do not).