To enforce the feeling that different tabs are on the same screen you should not use the default animated activity transitions between the tabs (users associate them with moving deeper into the app). The tabs are side by side and any animations used should reflect that. The best animation is sliding animation. This also encourages users to use swipe gestures to move between tabs.
Typically, users don’t need to simultaneously see content from multiple tabs. If your content requires people to compare the info from the different tabs, then better no to use tabs at all, because switching back and forth increases users short-term memory load and lowers usability.
Modals and mobile devices usually don’t play well together. Viewing the content is difficult because modals either are too large, taking up too much screen space or too small. Add in elements like the device keyboard and nested scrollbars; users are left pinching and zooming trying to catch the fields of a modal window. There are better alternatives for modals and shouldn’t be used on mobile devices.