Question 1: Does the gain of an antenna always increase with the
decrease in directivity?
Real antenna gain is nearly always referred to the theoretical isotropic antenna. The isotropic antenna emits power in all directions equally therefore it projects power onto the surface of a sphere where the antenna is at the centre of the sphere.
At distance r (radius of sphere), the power from an isotropic antenna is passing thru a spherical area of \$4 \pi r^2\$ square metres.
Normal antennas (such as dipoles) do not transmit this power in all directions therefore they are said to have a gain in certain directions compared to the isotropic antenna and, indeed there is more power per sq metre at a comparable distance, but this is beginning to become "directional". Therefore the higher the directionality of an antenna, the more power it concentrates in one direction (reciprocal for receiving antennas too) and the higher the gain.
Question 2 : What type of GSM antenna is recommended for an
application that can run in such low GSM coverage areas?
What is the likely incident power received and what is the minimum power needed by the receiver. A good figure for required power by the receiver is based on the signal data rate: -
Received power is -154dBm + 10\$log_{10}\$(data rate) - from this you can calculate the headroom, add maybe 20 dB for fade margin (could be lower if you accept a longer delay and you are moving).
Question 3 : What sort of an effect would the animals giant body have
in the reception of GSM signals? If yes, what are the remedies I can
do to reduce the impact of the same.
I have no idea.
Antennas are reciprocal - they transmit and receive equally well (or poorly).
The reason it's important to tune a transmit antenna is because a mistuned antenna, by reflecting power, can destroy the transmitter output stage.
Tuning a receive antenna is much less important, compared to that!
Most receive antenna tuning is frequency sensitive, in fact in the crystal set days, the antenna was often part of the first tuned circuit, and re-tuned for each new station.
With a broadband antenna, there's really not much point making such adjustments.
However you can improve reception by:
if the received signal is weak, increase its height, or use a larger antenna better suited to that waveband.
if it's strong but contains interference, use a directional antenna to reduce the interference - or add a tuned circuit to reject the interfering frequency.
and so on.
These can make big differences in reception. If we knew what you are specifically interested in receiving, you may get more specific answers.
Best Answer
Simple question first:
Antennas are reciprocal. So, the same benefit you get on TX, you'd typically get on RX.
That was a simplification, because:
Well, in the main beam, you get 4 dB more signal power. If your 9dBi antenna really is that much better than your 5dBi antenna.
However, whether that translates to a higher data rate.
Data rate is certainly limited by the SNR at your receiver; which, at constant noise level, is defined by the amount of power reaching your receiver's antenna.
However, that is but one of many factors that limit rate.
First of all, a receiver antenna with a high gain might also be getting more sensitive to an interferer that happens to also be in the main lobe now. Remember, you're in an ISM band, so everyone is allowed to communicate on your WiFi channel.
In a normal indoor scenario, it's not that the signal between your transmitter and your receiver only takes the direct path – it gets reflected on furniture and walls (especially steel armaments on those), and thus, you get a complicated multipath scenario. Classically, this is really a problem: Because these multiple paths have different lengths, the signals overlay, and might as well cancel out. Giving your transmitter a higher-gain antenna probably makes the shortest path better, but that doesn't mean things work better overall - it's very very hard to predict how the different path signals will overlap. And maybe, due to cancelling of the direct path with a path that is just half a wavelength longer, your receiver signal actually gets weaker because you use a higher-gain antenna.
Many modern access points and better WiFi adapters use what is called diversity gain with multiple antennas ("MIMO receivers"). Those actually benefit from the multiple paths – because each path has different properties, clever algorithms allow to get through more bit/s. But: for that you'll actually need the paths. In a bad-luck situation, your 4dB gain is actually decreasing your rate.
All in all, even if the additional 4dB directional gain actually just have the maximum benefit they can, i.e. they increase SNR by 4dB (\$=10^{\frac4{10}}\$), the harsh truth is that your expected (note: stochastic property!) increase in channel capacity can be bound by the ratio of Channel capacities with 5dBi and 9dBi antenna:
$$\begin{align} \frac{C_{9dBi}}{C_{5dBi}} &= \frac{B\log_2(1+\text{SNR}_{9dBi})}{B\log_2(1+\text{SNR}_{5dBi})}\\ &= \frac{\log_2(1+\text{SNR}_{5dBi}\cdot 10^{0.4})}{\log_2(1+\text{SNR}_{5dBi})}\\ &\approx \frac{\log_2(1+2.5\text{SNR}_{5dBi})}{\log_2(1+\text{SNR}_{5dBi})}\\ \text{for } 1 &\ll \text{SNR}_{5dBi} \\ &\approx \frac{\log_2(2.5\text{SNR}_{5dBi})}{\log_2(\text{SNR}_{5dBi})}\\ &= \frac{\log_2(2.5) + \log_2(\text{SNR}_{5dBi})}{\log_2(\text{SNR}_{5dBi})}\\ &= \frac{\log_2(2.5) }{\log_2(\text{SNR}_{5dBi})} + \frac{\log_2(\text{SNR}_{5dBi})}{\log_2(\text{SNR}_{5dBi})}\\ &= \frac{\log_2(2.5) }{\log_2(\text{SNR}_{5dBi})} + 1\\ \end{align}$$
Which means that your 9dBi antenna gives you a rate increase by \$\frac{\log_2(2.5)}{\log_2(\text{SNR}_{5dBi})}\$.
Plug in "normal" SNRs for WiFi:
If your SNR now is \$15dB= 10^{1.5}\$, and with \$\log_2 2.5 = 1.3\$, your rate gain is a meagre \$\frac{\log_2(2.5)}{\log_2(10^{1.5})}\approx \frac{1.3}{5}\approx 26\%\$.
If your receiver SNR is \$30dB = 1000 \approx 2^{10}\$ now (so already pretty OK), your rate gain is only \$\frac{\log_2(2.5)}{\log_2(2^{10})}\approx \frac{1.3}{10}= 13\%\$.
All in all, unless you already have very weak reception, the 4dB won't do much good. And if you have really weak reception, either a really high-gain antenna will help (because you're at the wrong end of the block, for example), but you'd have to be careful not to break the law with that, or actually more antennas. So, getting a proper MIMO system with at least two antennas on each end will very likely yield better results.
This is especially true because for WiFi, the problem usually isn't receiver noise (thus, SNR), it's interference on the ISM band (thus, SINR). And MIMO actually (almost) always can help with that, whereas it's really a random game whether a high gain antenna is the solution to an interference problem in a dense network. In fact, you can even make the so-called hidden-station problem worse by making one end of the communication link "deaf" to interferers that are very strong for the other end with a high-gain antenna. And such a problem typically isn't visible as signal strength metric, but leads to broken transmissions, and those are always far more expensive than having a slightly worse SNR.