Shimano 105 9 speed shifters.. When changing to a smaller cassette ring, i have to push the "inside" black plastic lever back... it stopped springing back automatically as its supposed to do. Any suggestions please? Thanks

Could be just an over-tight cable.. or the limit screws at the gear end over-tightened so that the selector does not transverse the full width of the gear cluster cassette...

Shimano has technical documents available for most parts.
Here is the page for the 105 groupset:
http://techdocs.shimano.com/techdocs/blevel.jsp?FOLDER%3C%3Efolder_id=2534374302051113
And here is the pdf for the freehub/cassette
http://techdocs.shimano.com/media/techdocs/content/cycle/SI/105/FH-5500-5501/SI-32X0D-En_v1_m56577569830612169.pdf

Derailleurs have a return spring in them that will always return them to the smaller cog (whether it is front or rear). The derailleur cable resists this spring tension. If your front der. is on the large ring and will not shift to a smaller ring then it could be a couple things. First, too much cable tension preventing the spring from returning the derailleur to a smaller cog. Second, you low limit screw is set too far in so the derailleur cannot travel back to a lower gear. This will be evident if you shift to a smaller cog, the derailleur does not move and the cable becomes slack. Third, something else is preventing the derailleur from moving, perhaps the derailleur was moved when installing the new crankset and it is getting hung up on a tooth of the large chainring, there could be some foreign matter lodged in the derailleur spring preventing it from operating, the spring could have broken so there is no longer enough tension to move the derailleur back to it's "home" position. Good luck.

Try flushing out the shifter(s) with WD-40, use plenty. The next step will be replacing the shift cables and cable housings.

• Take the bicycle in an area free of cars and obstacles, such as an open parking lot. Concentration is required when learning to use Ultegra shifters or any other type of bicycle shifter.
  
• 2 Mount the bicycle and rest both hands on the proper Ultegra hand control. The left-hand control operates the front derailleur. The right-hand control operates the rear derailleur.
  
• 3 Start pedaling, smoothly and evenly. While pedaling is crucial to propelling the bicycle forward, it is also necessary when shifting the derailleur. Pedaling forces the chain to rotate. The chain must rotate before it can transfer to another gear.
  
• 4 Push the outside right Shimano Ultegra lever in toward the bicycle. The rear derailleur will shift the chain to a smaller rear gear.
  
• 5 Push the inside right Shimano Ultegra lever in toward the bicycle. The rear derailleur will shift the chain to a larger rear gear.
  

Rear Ultegra Derailleur Control

• 1 Push the outside left Shimano Ultegra lever in toward the bicycle. The front derailleur will shift the chain to larger front gear.
  
• 2 Push the inside left Shimano Ultegra lever in toward the bicycle. The front derailleur will shift the chain to a smaller front gear.
  
• 3 Use the front and rear Ultregra hand controls interchangeably. For small changes in gearing, using the rear control. For larger changes, choose the front control. A smaller gear causes the bicycle to travel a shorter distance per pedal stroke but also requires less energy to use. A larger gear requires greater effort but in turn causes the bicycle to travel farther per pedal stroke.
  

Any 9spd Shimano STI brake lever hoods will work. Do a search on the web for: Shimano 9spd lever hoods.

Barrel adjusters on road bikes are usually where the cable enters the cable stop at the top of the down tube. They're for ON-THE-FLY adjustment trimming, not overall adjustment.

You need a basic adjustment...

http://www.parktool.com/blog/repair-help/categories/derailleur-systems

The problem is not with the derailleur tension - that is preset. If the levers worked properly on your wife's bike you may have the cable set just a bit too tight, so that there is too much tension against the outer limit stop when you shift to the large chainwheel. Try backing off the high limit screw. If you can then shift down OK you need to loosen the cable clamp and let the cable slip very slightly looser (and then restore the proper outer limit adjustment). If there's still a problem then the only culprit is the lever.

I’m happy to help further over the phone at https://www.6ya.com/expert/donald_f2ed37026a3ac881

No -

If you are going to use the front triple crankset, then you need to use the 6603 components. These are for Triple set-ups.

If you intend to keep your bike a triple, then everything in the drivetrain must be the triple designation, hence the XX03.

If you want to change the crankset to a compact, then you can use the 6600 (double) equipment, but you will need to change the left (front shifter) to a double as well. The compact crankset, will give you virtually the same range as the triple and be much lighter and shift better.

The cassette: You can use any 10 spd cassette from Shimano or SRAM as long as the rear cog is no larger than 27. if you want to use a larger cog like a 28, then you will have to use the 6700 group, assuming yoiu want to stay with shimano ultegra.

Final Note: Since you are chainging everything, you may want to consider the SRAM Apex group, this gives you more gear ratio than the Ultegra, is slightly less expensive and around the same weight. Great alternative to Triple bikes.

Parts you will need to convert:
Rear Derailleur
Front Derailleur (if changing to compact double or Apex)
Chain
Shifter set (if Apex)
Crankset (if Apex or compact shimano)
Bottom Bracket (if Apex)

The biggest thing is that Shifters and rear derailleur must be from the same company (shimano, SRAM, etc.) after that just make sure that yoiu use 10spd with 10spd, 9 with 9, and so on. Everything else can mix and match.

Could actually be both. Squirt a small amount of lubricant between the two paddles and shift one or the other multiple times to see if they free up. If not you made to take it to your local shop where the can disassemble the shifter to see if debris has lodged itself inside.

It sounds like you could have two different problems. Your derailleur has become contaminated or your shifter may need to be lubed. Either way, the likely solution is the same. The best solution to get the derailleur operating again is to spray it with GT-85 or PB blaster and manually move in back and furth until it is working again. The same goes for the 105 shifter, spray GT-85 inside the shifter by compressing the brake lever and spraying towards the head of the shift cable. This will solve a non-functioning shifter many times.

The only other problem that fits is the limit screws could be wrong or the deraileur is in the wrong position. This would not be the case unless someone adjusted your derailleur before the ride you started have that problem. Or if the derailleur has moved. Both of which require the derailleur to be fully readjusted.

Hope this helps. Thank you