Adding my wifi router wired to an existing router on a public network?

[lectrocrew]

 I just moved into a new apartment that includes free WiFi in the rent. But it is a public network that, from my understanding is only secured behind the router via password, but not within the network itself. So I asked the owner to connect my Netgear N150 router input wired to one of the wired outputs on the public network router (also a Netgear). The public network owner (my landlord) said he knows little about computers etc and said he would ask the man who manages his network about adding my router as I described.
 That man may have some questions such as:
 (1) will this affect the service from the ISP in any way?
 (2) will it make his network less secure or affect it negatively in any way?
 etc etc etc.
I would think it would not affect his wifi, and will even help the speed since this will make 1 less device on that wifi network (there are 8 devices on it now) - (mine will actually be wired as far as his network is concerned).
 
 So won't this then make the 802.11n signal from my router secured from his public network via my password? Therefore, I then can network my 2 computers safely behind my router?

I'm not very knowledgeable about all this and what I described is just my interpretation of how it works. So where am I misinformed and what should I tell him about doing this?

 I do some volunteer medical oriented work with some individuals who share sensitive medical information with me therefore I cannot do this work on a public network, so a solution for this is very important to me, and to the ones I work with. So as always, thanks for any help on this matter. 

[Geek-9pm]

Even while  on a public network you can have a level of protection from intruders.
There are a number of  articles s on this topic. Here is one:
How to Stay Safe on Public Wi-Fi
Perhaps that may help.

[lectrocrew]

 Thanks for the link but I really want this router installed if it's not going to cause a problem. I just realized that this also may increase my connection speed - there are 4 users using this network right now and it's slow.
 So if I install my router, I will reduce any slow issue due to activity volume limits of the wifi transmission. Instead, I will have 100% of the wifi transmission from my router for myself only, and this will be limited only by the volume constraint of the wired connection limit through the router. Correct.
 So is doing this going to cause any problem?

[Geek-9pm]

Your assumptions are not supported by facts. Internet speed is set by the ISP. It is not a function of the router. (Unless you have fiver optical cable.)
If the router is of good quality, the rule is:
"When there is one active user, the full speed of the network is available."
Time division works only when other users are active. It is a dynamic system.

About having more that one router in a home or small business network. Personally I have only used three routers  in my local network. Mostly because of the distance of the cable. Runs under 100 feet between routers are preferred. with 300 feet being the piratical maximum with good cable.

Only one router can control DCHP. (You can make an exception, but it is not worth the effort.)

Because  my personal experience is l limited, maybe an active IT person will tell you how to improve security with two routers.  Cost would be a factor, otherwise you would just buy your own service. In an enterprise network there are ways to split up the network and improve privacy.  This is costly for a small local network.

What I am say s that if privacy is a high issue, the use of a separate service is recommended.

Just trying to help. 

[Geek-9pm]

Doing some research, some say its OK to use two routers on small network.
How to Connect Two Routers on a Home Network

This guide explains how to set up a router for home computer networks. The exact names of configuration settings on a network router vary depending on the model and whether it is wired or wireless. However, this general procedure will guide you through the process for the common kinds of home network equipment.

Let me know if that is what you want. 

[lectrocrew]

We are getting there. Most of this I already know. I have used multiple routers before and it was nothing more complicated than pluging in the power adapter and the ethernet cable. The 1st router then assigns an IP Address to the 2nd router just like it would if it was an additional PC. That's all there is to it in most situations.
 
 But the type of things that I was looking for answers to is that I had forgotten that sometimes it is necessary to change the channel on which the 2nd router operates in order to limit the chance for radio frequency interference between the 2 routers. It's very possible this will be needed in my case because both routers are the same model made by the same manufacturer.
 
 Can anyone else think of any issues I may encounter? If I connect this and it causes a problem, then my new landlord may not give me an opportunity to go back and change channels or whatever else is a problem. I need it to be right the first time.

 

[Geek-9pm]

The routers should have at least a spacing of one meter or more physically. The channel spacing should be 3 or more . Example, Ch 5 and 9. Or Ch 3 and 6.

[lectrocrew]

Got it installed and working fine. This makes my two PC's the only two on my network so that's what I want. Default router access password has been change from default to my preference as well as SSID and WiFi login password.
 There are seven different routers within range of my wifi location (highly populated residential area), I set my router channel to 9. The closest other router set to channel 9 are two routers on 6 and one router on 11.
 So thanks Geek-9pm for the help once again. I'm happy to be on a private network and now I have a bunch of secure work to get caught up on....