Your paste is fine. The problem is that you are applying way, way, WAY too much solder paste. I’m guessing at least 5 times as much as you need.
It’s really hard to apply paste in controlled amounts by hand using a syringe (there’s literally special equipment just to help with that), so either accept that you will need to rework it afterward, or just make your life easier and use a stencil.
What will help with syringe use is very fine conical tips. They require much less force than needle tips. (I’d recommend getting some 25ga (0.26mm) conical tips.)
Take a look at some photos and videos of solder paste applied by stencil. You’ll see it’s a thin layer applied to less than the full area of the pad. (A typical stencil is 0.125mm thick or less!) That should give you an idea of how little solder paste you actually need.
Okay, it's good to know my paste is fine. The syringe is for T3, so not very fine. I will try the conical tips with a smaller opening. My hands are very shaky so I have troubles applying paste perfectly without tools. I have avoided stencils since they are more expensive than a full set of PCBs. I will try them next time I order a batch of PCBs.
I do recommend storing your paste in the fridge. It'll last longer.
FYI, your T3 paste is ideal. Finer paste, while necessary for
extremely small stencil apertures (for pads far smaller than anything you'd ever consider doing by hand), is actually
more susceptible to bead creation, and its shelf life is shorter.
Shakiness: if you can get a decent
optical (not digital) microscope to work under, you will find that you shake far less.
Stencil cost: I understand. For a one-off board that can be soldered by hand, I often skip them too. But for anything where you either a) need to make a bunch of them, b) have components that cannot be hand-soldered easily, or c) where you want to minimize the risk of assembly problems, a stencil is a big help.
Something I have done in the past to save cost on the stencil (especially for larger boards, where the sheer size of the stencil ends up substantially increasing the shipping cost from China) is to create a partial stencil only. For example, I had a board with three identical channels, so I just ordered a stencil for one channel and used it three times.
Note also that the openings in the stencils need to be smaller than the pads. 15% reduction is typical, but for stencils used by hand -- that is, not in a stencil printer -- a bit of paste can often squeeze under it, so I've had the best results with 20-25% reduction. Or you can order a thinner stencil if your manufacturer offers it. Large hidden pads (like ground/thermal pads under QFNs) need even less paste, often around 40% reduction.
Most PCB manufacturers will reduce the openings by 10-15% by default. If you want them reduced more, either tell them to do that, or tell them to not reduce them at all, and reduce them yourself in your PCB layout.
Another approach I've used with decent results is to apply paste by hand, but to clean it up carefully
before reflowing. I use a curved scalpel blade (with no force applied) as a scraper to pick up and remove excess paste. What is quite important, possibly more important than the absolute amount of paste, is that the amount of paste be even on the pads of a part, so that the part doesn't tombstone or get pulled away once the solder melts.
For example, on chips with entire rows of pins (SO, SOIC, QFP, QFN, etc), I will lay down a "noodle" of paste across a whole row of pins. I start squeezing on the board a cm or two before the first pin, then lift the syringe tip so the noodle is actually squeezed out in the air, which keeps it nice and straight, and then lay it down across the entire row of pins, ending a few mm after the last pin of the row. Starting and ending outside of the row of pins keeps the amount much more even, since the ends tend to have blobs. Then I use the scalpel to "trim" the noodle to one pin's width longer on each end, and then scrape the excess paste away.
You can similarly use a scalpel blade to remove excess from the pads of resistors, caps, etc.
With that said -- because boards reflowed with syringe-applied solder paste often need lots of rework with the soldering iron anyway -- if possible, I just solder them with the soldering iron to begin with.
Invest in some soldering iron tips for rework. For this type of work, I really like PLCC blades (often called a "knife" tip), since their edge can fit into nooks and crannies to pull away excess solder. I've attached a picture of the PLCC blade my soldering iron uses, so you can see the tip shape I mean.
Also make sure you have a good gel/tacky flux, which makes a world of difference during rework. For example, MG Chemicals 8341 or Chip-Quik SMD291NL (my favorite so far). A liquid flux pen is also handy on occasion.