Hashmap with Streams in Java 8 Streams to collect value of Map

What you need to do is create a Stream out of the Map's .entrySet():

// Map<K, V> --> Set<Map.Entry<K, V>> --> Stream<Map.Entry<K, V>>
map.entrySet().stream()

From the on, you can .filter() over these entries. For instance:

// Stream<Map.Entry<K, V>> --> Stream<Map.Entry<K, V>>
.filter(entry -> entry.getKey() == 1)

And to obtain the values from it you .map():

// Stream<Map.Entry<K, V>> --> Stream<V>
.map(Map.Entry::getValue)

Finally, you need to collect into a List:

// Stream<V> --> List<V>
.collect(Collectors.toList())

If you have only one entry, use this instead (NOTE: this code assumes that there is a value; otherwise, use .orElse(); see the javadoc of Optional for more details):

// Stream<V> --> Optional<V> --> V
.findFirst().get()

For your Q2, there are already answers to your question. For your Q1, and more generally when you know that the key's filtering should give a unique value, there's no need to use Streams at all.

Just use get or getOrDefault, i.e:

List<String> list1 = id1.getOrDefault(1, Collections.emptyList());

If you are sure you are going to get at most a single element that passed the filter (which is guaranteed by your filter), you can use findFirst :

Optional<List> o = id1.entrySet()
                      .stream()
                      .filter( e -> e.getKey() == 1)
                      .map(Map.Entry::getValue)
                      .findFirst();

In the general case, if the filter may match multiple Lists, you can collect them to a List of Lists :

List<List> list = id1.entrySet()
                     .stream()
                     .filter(.. some predicate...)
                     .map(Map.Entry::getValue)
                     .collect(Collectors.toList());