There is quite a learning curve to it all, in particular with carbide and the inserts. I am not sure what your are trying to determine machining between centers with HSS, the finish is pretty horrendous which suggests the grind is not correct and also the nose radius it to sharp for the feed. The issue of the taper, just indicates your tailstock position is not set correctly. As far as carbide and SFM, yes there is a sweet spot as to SFM, but there are many other important factors that effect finish. I will assume you are running TNMG inserts or negative rake, these take more Hp and a more substantial DOC and feed to remove the metal, neutral rake tooling or inserts with a tilted up edge with chip breaker typically used for finishing will give a cleaner cut at lower SFM. Still a lot depends on the edge geometry, coating, chip breaker, etc. Most of the insert boxes give you a range of feed and SFM typically designed for maximum material removal over the shortest time with good insert life. This is based on optimum tool geometry and system rigidity, but on SFM I am often in the 50-75% of rating for that material. Also the SFM and feed is very dependent on the materials, and some it like CRS tends to be a bit challenging to get a decent finish. If you are getting a lot of chatter, then your RPM is probably too high, so slow it down and play with the feed and DOC. The ideal swarf are C-shaped curls that break into pieces, but you may also get longer strands of swarf in particular with tougher metals like the 4000 series. I have attached a partial file from TMX which gives a lot of information as to general insert characteristics, feeds and speeds.
I would take a sample of 2 or 3" round material and just use the chuck with maybe 5-6" of stick out. Take a pass at say 0.004 vs. 0.008 IPR start at 400 RPM, 600, 800 RPM with say a 0.050" DOC. Start to find what gives you a better finish and the desired chips. Steel chips should becoming off straw color and turning blue. There are different types of inserts for different finishes and materials, some will cover a range. Often, in particular the TNMG which are considered obsolete by many mainstream shops, old stock is sold for pennies on the dollar. I can tell you that what works on steel will not work well on aluminum and softer materials, stainless and exotic materials requiring sharper cutting edges that are durable which much lower SFM and higher feed. Do not expect one insert to do it all under all conditions. Look at the attached document, review the basic coating, shapes, nimencalutre and cutting paramters in the materials listed. I usually run lower SFM and adjust the feed and DOC.
Don't ever forget about safety glasses and wear a baseball cap also . If you ever get a chip hang up behind those glasses , you'll wish you were on a scooter with a wasp in your helmet ! 
