I'll answer both of your bolded questions:
- Google Analytics
Using Google Analytics you consent to their terms of service which state that you, using Google Analytics, will have and abide by a privacy policy:
You will have and abide by an appropriate Privacy Policy and will
comply with all applicable laws, policies, and regulations relating to
the collection of information from Visitors. You must post a Privacy
Policy and that Privacy Policy must provide notice of Your use of
cookies that are used to collect data. You must disclose the use of
Google Analytics, and how it collects and processes data.
Therefore, you always need a privacy policy no matter what you do with your Google Analytics installation. This is rooted in privacy laws around the globe, Google just codified this.
The privacy policy on the app store and in the app as a minimum is a no-brainer. Even just to say in plain English that this app doesn't collect and process any personal data.
The bigger question these days leading up to September 30th is, whether you need to abide by the stronger wording of the EU user consent policy when you target European users.
The answer is yes, when you use any of the Google Analytics Advertising Features:
When using Google Analytics Advertising Features, you must also comply
with the European Union User Consent Policy.
For apps this realistically comes down to collecting consent before starting the app and collecting any data.
- Cookie law is only concerned with websites
As pointed out by @Eike, the cookie law isn't necessarily concerned with cookies or websites as such, it extends to cookies and similar technologies. Here's what the Article 29 Working Party says in its communication regarding cookie consent exemptions:
requiring informed consent before information is stored or accessed in
the user’s (or subscriber’s) terminal device. The requirement applies
to all types of information stored or accessed in the user’s terminal
device although the majority of discussion has centred on the usage of
cookies as understood by the definition in RFC62651. As such, this
opinion explains how the revised Article 5.3 impacts on the usage of
cookies but the term should not be regarded as excluding similar
technologies.
It says two things: not only cookies, but all similar technologies, not only web but all terminal devices.
To come back full circle, in their EU user consent policy Google mentions both websites and apps in order to make sure everyone understands the requirements:
If the EU user consent policy applies to your website or app, two of
the key things to consider are:
- Do you have a means of obtaining consent from your end users? If not, you’ll need one.
- What message should you present to your users to get consent?
To finish, if you have some time you might want to check out this opinion on apps on smart devices.
disclosure: It is a very complex topic that I'm working on daily at www.iubenda.com