1. How do modern low-cost GNSS receivers compare?

We prepared a simple comparison table and saved it below:

Receivers Table

This is intended as a simple quick overview and should by no mean taken as reference for cost sensitive system evaluation.

2. What kind of antenna should I use with my receiver?

This is probably the most frequent question. It makes a lot of sense, especially for products oriented to the high-precision market. 
The reality is that most of the times a low-cost antenna on a 20cm diameter ground plane will suffice.
Sparkfun sells a very good one which is I have proven working smoothly with Yuan10, Rappen10, SdrNav00, and others.
Please note that Sparkfun has lots of distributors around the World so if live outside the US please check those in your Country to avoid paying high shipping fees.
A very good antenna survey has been done by the RTKLIB team in Tokyo and can be found here.

If you are looking instead for a GPS/Glonass antenna to pair to your Denga receiver, the choice is very broad. In no orderwhat-so-ever there are Beyondoor, MaxtenaTaoglas, Tallysman, Antcom, and a million others (if you want to be added to the list feel free to contact us).
Please note that by default the NV08C-CSM outputs 2.85V on the RF antenna pin, which is a little lower than the most standard voltages for LNAs out there.

3. Why can pseudoranges be negative?

Pseudoranges are called "pseudo" because they are intrinsically affected by a bias, which is the clock bias between the receiver clock and the satellite clock.
The satellite clock is an atomic type clock with very good long-term stability and constantly monitored and maintained by the GPS ground control centre. The receiver clock is usually an oscillator with good short-term stability (e.g. TCXO).
The two are by system design non-synchronised and their bias is determined as part of the position solution: in fact the user needs 4 satellites instead of only 3 to determine his/her position in 3D - which geometrically would suffice in a completely synchronous system.
Usually receivers steer their clock to maintain their bias within a certain range (e.g. 10ms). If they don't the clock bias between the receiver and the GPS time can become quite large. A clock bias of about 76ms corresponds to 23e+3 Km, which is the average value of the true geometric range between a user on Earth and the GPS satellite. In such case, pseudoranges assume a value twice as high as the real geometric ranges, or become negative.
If you own a S1315F-RAW you may observe negative pseudoranges and RTKLIB will discard them. Simply issue a "reset to factory defaults" on GPSViewer to re-initialise the clock bias to a smaller value.