Can anyone point me to information on how to use more native platform elements (or more suitable ones) if the device is a mobile one?
There are also mobile UI toolkits: https://www.google.de/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=mobile%20ui%20framework
Also check out How to have different views for Mobile and Web Version? - #5 by fxckdead.
Also, how are people handling low/no connectivity situations?
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Show the user that the app is currently offline (Meteor.status)
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Meteor already handle queuing. So you can call a Meteor.method when you are offline and it will be transferred to the server when the connection was reestablished.