no. best way is millennium station to purple line and get off at Quincy. or better yet, take a cab.
I am assuming that by "owntown metra station" you mean "Ogilvie Transporation center". This is the main metra station. It's only about a block away. Inside Ogilvie, go to the Madison st main entrance. Exit and turn left on Madison st. Walk to the end of the block (Canal St) and Union station is right across Madison st. at the intersection of Madison & Canal. Good Luck!
Between 12:15 and 12:45, depending on line. Only the Milwaukee West and North, and Burlington, run on Sundays.
http://metrarail.com/Sched/cnw_nw/cnw_nw.shtml This site shows you metra trains to and from Chicago on the Union Pacific District Northwest line.
You would have to get over to the Union Station area. You have three ways to get to Milwaukee from downtown: 1) Megabus. This is the most frequent and usually the cheapest way to go. The bus stop is located across the street from Union Station. It is on Canal Street between Jackson and Van Buren. If you are taking a Metra or South Shore train to Millennium station, get off at Van Buren (the stop before Millenium Station) instead. Walk about a mile West (away from the lake) to Canal and then look for the crowd to your north on the east side of the street. If you are at Millennium station for some other reason, walk south on Michigan to Jackson, then turn right and head to Canal. Megabus tickets must be purchased in advance and are available only on their web site. If these directions are confusing, there is a map on the Megabus web site or take a taxi. 2) Greyhound. There are a few buses a day, prices are competitive with Megabus, but are usually a bit higher. The terminal is at 630 W Harrison St. Harrison St is two blocks south of Van Buren. Walk west on Harrison, a little more than a mile. It is two blocks west of Canal Street. 3) Amtrak. Amtrak operates several trains a day. It is the most expensive option, but not by that much. Amtrak operates from Union Station which is just across the street from where Megabus stops. All three go to the Milwaukee Intermodal Station on 4th and St. Paul. Megabus stops across the street. Greyhound and Amtrak stop inside.
Metra, which is the Chicago area's commuter rail system, stops near the Great Lakes naval station. The Metra line that goes there is the Union Pacific North line (or UP-North) which ends in Kenosha, Wisconsin. It departs from the Ogilvey Station just west of the Loop in downtown Chicago. The stop for the Naval Station is named "Great Lakes," and is about 75 minutes from downtown on a non-express train. Express trains cut that time to about 45 minutes. You can explore your options here: http://metrarail.com/Sched/cnw_n/cnwn.shtml
Chicago Union Station is open from 5:30 a.m. to 12:40 a.m. everyday. The last Metra trains out of Union station are at 12:40 a.m. and the last Amtrak train is at 8:05 p.m. (Milwaukee). The last arriving Amtrak train is at 11:10 p.m. (St. Louis). The next Amtrak train isn't until 6:00 a.m. (Milwaukee). The Amtrak ticket office is open 6:30 a.m. to 9:00 p.m. Metra police aggressively chase people out of the building at about 1:00 a.m. The food court closes at midnight. A couple of hours after the evening rush is over, there is basically just a trickle of people coming and going. It's not dangerous inside, if that is what you are worried about.
Union Station opened on October 27, 1907
Union Station - Dallas - was created in 1916.
Memphis Union Station was created in 1912.
Hartford Union Station was created in 1889.
Waterbury Union Station was created in 1906.
Goldsboro Union Station was created in 1909.