I'm a regular visitor to Chattanooga and I can help with a handful of your questions.
1. NS runs around 70 trains a day through Chattanooga. That includes trains originating and terminating at DeButts Yard, locals, and through trains. CSX will run about 20 a day. Below, I'll include train symbols, trains according by route, and their average train counts.
3. Besides the spots you included, I would recommend the area around Nickajack Lake, just west of Chattanooga. The CSX mainline borders the lakefront and NS has trackage rights on this route. In my opinion, this is one of the most scenic areas in the area. I also recommend Wauhatchie. Wauhatchie is in the valley west of Chattanooga on the opposite side of Lookout Mountain. Both NS and CSX run through the area. NS' lines to Birmingham and Memphis diverge here. The AGS to Birmingham runs south while the Memphis line joins up with CSX on its way west. CSX's Wauhatchie Yard is located nearby. It's CSX's base of operations for Chattanooga and northern Georgia. Another spot is Ooltewah, just east of Chattanooga. This is where NS' line to Knoxville and Atlanta diverge. If you're willing to drive a little bit, Dalton, GA is another excellent spot. There's a railfan platform overlooking the NS and CSX mains.
4. Of the spots mentioned above, I've only stayed overnight at Dalton. Fellow railfans have done overnight railfanning at Ooltewah and the crossing at Jersey Pike Rd with few issues. Coffey's Cliff is excellent for daytime railfanning, but I was advised to to linger there too much longer after dark.
5. Other rail attractions include the Tennessee Valley Railroad Museum. Train schedules are included on their website. The Chattanooga Choo Choo in downtown is an interesting place to check out. There are a lot of non-railfanning things to do in the area such as Ruby Falls, Point Park, and Rock City. All of those are on Lookout Mountain. The Tennessee Aquarium is a very nice place and is well worth a visit.
Manifest trains that originate or terminate at DeButts Yard:
111 Kansas City, MO (BNSF) - Chattanooga, TN
116 Chattanooga, TN - Bellevue, OH
117 Bellevue, OH - Chattanooga, TN
123 Frankfort, IN - Chattanooga, TN
124 Chattanooga, TN - Decatur, IL
129 Chattanooga, TN - Birmingham, AL
130 New Orleans, LA - Chattanooga, TN
131 Knoxville, TN - Chattanooga, TN
132 Chattanooga, TN - Knoxville, TN
134 Chattanooga, TN - Linwood, NC
144 Chattanooga, TN - Elkhart, IN
147 Cincinnati, OH - Chattanooga, TN
148 Chattanooga, TN - Cincinnati, OH
164 Birmingham, AL - Chattanooga, TN
167 Venice, IL (TRRA) - Chattanooga, TN
168 Chattanooga, TN - Venice, IL (TRRA)
170 Chattanooga, TN - Conway, PA
177 Chicago, IL (BRC) - Chattanooga, TN
196 Chattanooga, TN - Detroit, MI
322 Macon, GA - Chattanooga, TN
325 Chattanooga, TN - Sheffield, AL
347 Chattanooga, TN - Atlanta, GA
348 Linwood, NC - Chattanooga, TN
361 Chattanooga, TN - Macon, GA
362 Sheffield, AL - Chattanooga, TN
363 Chattanooga, TN - Macon, GA
367 Chattanooga, TN - Birmingham, AL
370 Rome, GA - Chattanooga, TN
371 Chattanooga, TN - Rome, GA
Locals:
T41 Calhoun, TN - Chattanooga, TN
T44 Chattanooga, TN - Calhoun, TN
T78 Chattanooga, TN - Hickson, TN turn
T89 Chattanooga, TN - Wauhatchie, TN CSX turn
TC10 Chattanooga, TN - Collegedale, TN ? turn
TC65 Chattanooga, TN - Volkswagen turn
Run through trains:
Intermodal:
201 Rutherford, PA - Rossville, TN
202 Rossville, TN - Rutherford, PA
207 Savannah, GA - Memphis, TN (runs 2x a week)
215 Chicago, IL (Calumet) - Atlanta, GA
216 Atlanta, GA - Chicago, IL (Calumet)
223 Kansas City, MO - Atlanta, GA
224 Atlanta, GA - Kansas City, MO
229 Columbus, OH - Jacksonville, FL (FEC)
282 Jacksonville, FL - Chicago, IL (Landers)
285 Kansas City, MO - Jacksonville, FL (FEC)
295 Chicago, IL (Landers) - Jacksonville, FL (FEC)
22N Memphis, TN - Atlanta, GA
23N Atlanta, GA - Memphis, TN
25Q Atlanta, GA - Memphis, TN (runs 2x a week)
Autorack:
275 Shelbyville, KY - Atlanta, GA
276 Jacksonville, FL - Georgetown, KY
284 Jacksonville, FL - Princeton, IN (runs 1x a week)
288 Atlanta, GA - Detroit, MI
25J Atlanta, GA - Roanoke, IN (runs as needed)
Various empty autorack trains run to VW as needed
Run Through Manifest:
142 Birmingham, AL - Elkhart, IN
143 Elkhart, IN - Birmingham, AL
162 Sheffield, AL - Linwood, NC
163 Knoxville, TN - Sheffield, AL
174 Macon, GA - Elkhart, IN
175 Bellevue, OH - Macon, GA
178 Birmingham, AL - Bellevue, OH
179 Bellevue, OH - Birmingham, AL
15T Allentown, PA - Birmingham, AL
16T Birmingham, AL - Allentown, PA
334 Sheffield, AL - Macon, GA
335 Macon, GA - Sheffield, AL
397 Chicago, IL Colehour - Birmingham, AL
Train symbols by routes out of Chattanooga:
CNO&TP Third District
111, 116, 117, 123, 124, 142, 143, 144, 147, 148, 167, 168, 170, 174, 175, 177, 178, 179, 196, 215, 216, 223, 224, 229, 275, 276, 282, 284, 285, 288, 295, 25J, 397, T78, average 4 unit trains a day
Total average: 37 trains a day
Atlanta North District
174, 175, 207, 215, 216, 223, 224, 229, 275, 276, 282, 284, 285, 288, 295, 22N, 23N, 25J, 25Q, 322, 334, 335, 347, 348, 361, 363, 370, 371, average 10 unit trains a day
Total average: 34 trains a day
Memphis District East End
162, 163, 201, 202, 207, 22N, 23N, 25Q, 325, 334, 335, 362, T89, average 7 unit trains a day
Total average: 19 trains a day
Knoxville District West End
131, 132, 134, 162, 163, 15T, 16T, 201, 202, T41, T44, average 1 unit train a day
Total average: 12 trains a day
AGS North District
129, 130, 142, 143, 178, 179, 164, 15T, 16T, 367, 397, average 1 unit train a day
Total average: 11 trains a day