How to find where there are safety issues in Paris?

Risk areas

First, while there is a risk, it is obviously hard to tell about where any risk is present. Based on the events that happened in France in 2015 and particularly in Paris, one might make an assumption that cities have a higher risk than other parts of France. I insist (if this is not clear enough) on the fact that this is an assumption. From my impressions and discussions I had, the security measures are more applied in Paris than in the rest of the country. And as far as I know, resources do not make a difference between places (the only I thought of was the UK Government travel advice that, as of the end of December, explains the risks of Terrorism in France).

Security measures

For your second point, in Paris, just expect bag searches whenever you enter any building (museums, stores, sometimes university, really any places - I heard it may take place in train stations, so plan some extra time if you take a train, but so far I have not seen any). The new standard procedure is for everyone to show their bag content, open their jacket and rarely empty their pocket (at the Centre Pomppidou). Everyone is cooperative and there usually is not any issue, the security personnel is polite.

To tell you how extreme this may seem, I once went across a train station at rush hour time, i.e. full of people. Inside the station, I entered a small shop, with about 10 people inside, and the shop's security guard asked me to open my jacket. I was surprised that the shop owner was worried about some attack in this tiny shop while the station is crossed by thousands or maybe tens of thousands of people every day.

Overall, also expect many militaries and police patrols everywhere in the streets, in the metro and train stations, ...

Check for information

Regarding your last point, the public transit trafic information is available in real time on the homepage of the RATP website for the metro lines and some RER lines. There are also mobile apps to check trafic information like the app provided by the RATP. When you go across the city, most metro stations also have one or multiple screens with trafic information too, check it. Personally living in Paris, I check the trafic information every time I leave home or the office, to figure if there is any issue and I change my itinerary accordingly. There are A LOT of suspicious package alerts every day on the network, and that causes delay. People are patient and the trafic is usually OK within an hour, but it is always better to adapt.

If you are very cautious, you can also get a news app and check before you go out of a building to make sure nothing bad happened, but that may sound like paranoia now.

Overall, while there is always a risk, people are calm and patient about any security measure that might be taken. When travelling to Paris, behave in the same way, do not panic when the security personnel ask you to open your jacket, or when you see the police or military, that is now the daily life. If you are worried, check the news and public transit trafic information whenever you go out. That should be enough.