How does wiring two LNAs in parallel affect charactaristic impedance?
How does wiring an LNA in parallel affect the impedance on both sides?

I know that with &quot;wiring&quot; you mean &quot;connecting&quot;, but the link you add is a device that works at 45 MHz to 6 GHz. You don't model that as wires carrying current: You transport waves in waveguides. Seeing this package:

it's SMD, so this was designed for a PCB with microstrip transmission lines :)

Will it cut it in half and create 25-Ohm impedance values?

So, since you can't physically put them in the same position, the point where the impedance change happens is where you split that transmission line to go to both amplifiers, and the point where you combine the two transmission lines coming out of them.
These points actually have to be considered components with their own properties. We call them &quot;power dividers&quot; (or &quot;power splitters&quot;) and &quot;power combiner&quot;, respectively.
That power divider can be designed to e.g. have the same 50Ω input impedance as the two outputs. Also, it might be very interesting to not have power that reflected back from one of the amplifiers for any reason end up in the other (because that would be a great way of building a Gigahertz oscillator that you can not control).
Same goes for the power combiner at the output: you can make the output impedance be half or same as the input input impedance, by choosing an appropriate design for it!
In fact, the datasheet does say this:

• External biasing and matching required

So, your job is to first match the input impedance of the amplifiers to the transmission line coming e.g. from your antenna!
It might be easiest to do something like:

Have \$x\$ Ω wave impedance on your antenna trace. Want \$y\$ Ω wave impedance at the combined output (\$x\$ and \$y\$ can be the same, but don't have to be. For example \$x=75\$ and \$y=50\$ would be usual choices!)
match both amplifiers to \$\sqrt 2x\$ Ω impedance
Use a lossless power divider that converts the single \$x\$ Ω transmission line to two \$\sqrt2x\$ Ω transmission lines going to your amplifiers.
Match your amplifier's outputs to \$\sqrt y\$ Ω.
Combine with the same architecture as used as splitter above, but adjusted to output impedance of \$y\$ Ω and thus input impedance of \$\sqrt 2y\$ Ω.


It appears that wiring amplifiers in parallel improves the signal to noise ratio.

Generally, um, I'd be careful with that. The article you refer to doesn't apply to these RF LNAs, but to opamps on non-RF frequencies.
If you length match well enough and your amplifying devices really have the same phase (which can change with but a gust of warm air), then yes, combining the output of two amplifiers will lead to twice the signal power on the combiner's output, which is the presumption of the formulas given in that article. Sadly, that's hard, and often, you'll just cancel out some power of one amplifier by not phase-adjustedly the other.
If you want a better noise figure in an LNA, get an LNA with higher gain and the same low noise figure, or one with a lower noise figure and the same gain. LNAs tend to internall by really really simple devices - when you look at that datasheet, they even tell you it's but a single FET in a package. Why? Because, in general, every semiconductor junction you use to generate an output signal introduces more noise.
So, receiver system design is usually taking an LNA with a good noise figure and at least OK gain, and then cascading, not paralleling, more amplifiers if you need more power. I think wikipedia's Friis formula for noise article will come as a big enlightenment!
(by the way, the noise figure of this LNA is really quite excellent. Check thrice whether this is really the limiting source of noise in your whole transmitter-receiver signal chain before trying to optimize it. As always: requirements first, design later!)